A singular introduction to commutative algebra

A Singular Introduction to Commutative Algebra

Volumn , Issue , 2008, Pages 1-689

  Greuel, Gert Martin ^a   Pfister, Gerhard ^a   Bachmann, Olaf ^b   Lossen, Christoph ^b   Schönemann, Hans ^b  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^b NONE

Author keywords

[No Author keywords available]

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EID: 84892350521     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-73542-7     Document Type: Book

References (250)

1. Adams, W. W.; Loustaunau, P.: An Introduction to Gröbner Bases. Vol. 3. Graduate Studies in Mathematics, Providence, RI, AMS (1996).
2. Altman, A.; Kleiman, S.: Introduction to Grothendieck duality theory. SLN 146, Springer (1970).
3. Apel, J.: Gröbnerbasen in nicht kommutativen Algebren und ihre Anwendung. Dissertation, Universität Leipzig (1988).
4. Arnold, E. A.: Modular algorithms for computing Gröbner bases. J. of Symbolic Computations 35, 403-419, (2003).
5. Arnold, V. I.; Gusein-Zade, S. M., Varchenko, A. N.. Singularities of Differential Maps. Vol. I, Birkhäuser (1985).
6. Atiyah, M. F.; Macdonald, I. G.: Introduction to Commutative Algebra. Addison-Wesley, London (1969).
7. Aubry, P.; Lazard, D.; Moreno Maza M.: On the Theories of Triangular Sets. J. Symb. Comp. 28, 105-124 (1999).
8. Bachmann, O; Gray, S.; Schönemann, H.: A Proposal for Syntactic Data Integration for Math Protocols. In: Erich Kaltofen, Markus Hitz (eds.) Proc. of Second International Symposium on Parallel Symbolic Computation, PASCO'97, Maui, HI, USA, July, 1997. ACM Press, New York, 165-175 (1997).
9. Bachmann, O; Gray, S.; Schönemann, H.: MPP: A Framework for Distributed Polynomial Computations. In: Lakshman, Y. N. (ed.), Proc, of 1996 International Symposium on Symbolic and Algebraic Computation, ISSAC'96, Zürich, Switzerland, July, 1996. ACM Press, New York, 103-109 (1996).
10. Bachmann, O.; Schönemann, H.: Monomial Operations for Computations of Gröbner Bases. In: Proceedings ISSAC'98, 309-316.
11. Baciu, C.: The Classification of the Hypersurface Singularities using the Milnor Code. Diplomarbeit, Kaiserslautern (2001).
12. Bandman, T.; Greuel, G.-M.; Grunewald, F.; Kunyavskii, B.; Pfister, G.; Plotkin, E.: Two-variable identities for finite solvable groups, COMPTES RENDUS DE L'ACADEMIE DES SCIENCES, Ser. 1337 (2003) 581-586.
13. Bandman, T.; Greuel, G.-M.; Grunewald, F.; Kunyavskii, B.; Pfister, G.; Plotkin, E.: Engel-Like Identities Characterizing Finite Solvable Groups, Compositio Math. 142(2006), No. 3, 734-764.
14. Bayer, D.: The Division Algorithm and the Hilbert Scheme. Ph. D. Thesis, Harvard University, Cambridge, MA (1982).
15. Bayer, D.; Galligo, A.; Stillman, M.: Gröbner Bases and Extension of Scalars. In: Proceedings Comput. Algebraic Geom. and Commut. Algebra, 198-215, Cortona, Italy, Cambridge University Press (1991).
16. Bayer, D.; Mumford, D.: What can be Computed in Algebraic Geometry In: Proceedings Comput. Algebraic Geom. and Commut. Algebra, 1-48, Cortona, Italy, Cambridge University Press (1991).
17. Bayer, D.; Stillman, M.: On the Complexity of Computing Syzygies. J. Symb. Comp. 6, 135-147 (1988).
18. Bayer, D.; Stillman, M.: Computation of Hilbert Functions. J. Symb. Comp. 14, 31-50 (1992).
19. Bayer, T.: Computations of Moduli Spaces for Semiquasihomogeneous Singularities and an Implementation in Singular. Diplomarbeit, Kaiserslautern (1999).
20. Becker, T.; Grobe, R.; Niermann, M.: Radicals of Binomial Ideals. Journal of Pure and Applied Algebra 117 & 118, 41-79 (1997).
21. Becker, E.; Marinari, M. G.; Mora, T.; Traverso, C.: The Shape of the Shape Lemma. In: von zur Gathen, J., Giesbrecht, M. (eds.): Proceedings of the International Symposium on Symbolic and Algebraic computation. Association for Computing Machinery. New York, 129-133 (1994).
22. Becker, T.; Weispfenning, V.: Gröbner Bases, A Computational Approach to Commutative Algebra. Graduate Texts in Mathematics 141, Springer (1993).
23. Becker, E.; Wörmann, T.: Radical Computations of Zero-dimensional Ideals and real Root Counting. Mathematics and Computers in Simulation 42, 561-569 (1996).
24. Bermejo, I.; Gimenez, P.: On Castelnuovo-Mumford Regularity of Projective Curves. Proc. Amer. Math. Soc. 128 (5) (2000).
25. n using quotients of monomial ideals, JPAA 164 (2001)
26. Bigatti, A.; Caboara, M.; Robbiano, L.: On the Computation of Hilbert-Poincaŕe Series. Appl. Algebra Eng. Comm. Comput. 2, 21-33 (1991).
27. Boege, R.; Gebauer, R.; Kredel, H.: Some Examples for Solving Systems of Algebraic Equations by Calculating Gröbner Bases. J. Symb. Comp. 2, 83-89 (1987).
28. Brieskorn, E.: Die Monodromie der isolierten Singularitäten von Hyperflächen. Manuscripta Math. 2, 103-161 (1970).
29. Brieskorn, E.; Knörrer, H.: Plane algebraic curves. Birkhäuser (1986).
30. Bruns, W.; Herzog, J.: Cohen-Macaulay Rings. Cambridge University Press, Cambridge (1993).
31. Bruns, W.; Vetter, U.: Determinantal rings. SLN 1327, Springer (1988).
32. Buchberger, B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD Thesis, University of Innsbruck, Austria (1965).
33. Buchberger, B.: Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems. Äqu. Math. 4, 374-383 (1970).
34. Buchberger, B.: A Criterion for Detecting Unnecessary Reductions in the Construction of Gröbner Bases. In: EUROSAM'79, An International Symposium on Symbolic and Algebraic Manipulation (E. W. Ng, ed.). Lecture Notes in Comput. Sci., Vol. 72, 3-21, Springer (1979).
35. Buchberger, B.: Gröbner bases - an Algorithmic Method in Polynomial Ideal Theory. In: Recent trends in Multidimensional System Theory, N. B. Bose, ed., 184-232, Reidel (1985).
36. Buchberger, B.: Applications of Gröbner Bases in Non-linear Computational Geometry. In Trends in Computer Algebra, R. Janssen Ed., Springer LNCS Vol. 296, 52-80 (1987).
37. Buchberger, B.; Winkler, F.: Gröbner Bases and Applications. LNS 251, Cambridge University Press, 109-143 (1998).
38. Bueso, J.; Gomez-Torrecillas, J.; Verschoren, A.: Algorithmic methods in non-commutative algebra. Applications to quantum groups. Kluwer Academic Publishers (2003).
39. Campillo, A.: Algebroid Curves in Positive Characteristic. SLN 813, Springer (1980).
40. Canny, J. F.; Kaltofen, E.; Yagati, L.: Solving Systems of Non-linear Polynomial Equations Faster. Proc. Int. Symp. Symbolic Algebraic Comput. IS-SAC'92, ACM Press 121-128 (1989).
41. Caviness, B. F:: Computer Algebra: Past and Future. J. Symb. Comp. 2, 217-236 (1986).
42. Chèze, G.; Lecerf, G.: Lifting and recombination techniques for absolute factorization. Manuscript, Universit́e de Versailles Saint-Quentin-en-Yvelines, (2005).
43. Chrusciel, P.; Greuel, G.-M.; Meinel, R.; Szybka, S.: The Ernst equation and ergosurfaces. Preprint, http://arxiv.org/abs/gr-qc/0603041, 1-23 (2006).
44. Chyzak, F.; Salvy, B.: Non-commutative Elimination in Ore Algebras Proves Multivariate Identities. J. Symbolic Computation, 26(2):187-227 (1998).
45. Cohen, H.: A Course in Computational Algebraic Number Theory. Springer (1995).
46. Cohen, H.; Frey, G.: Handbook of Elliptic and Hyperelliptic Curve Cryptography. Chapman & Hall/CRC (2006).
47. Cohen, A. M.; Cuypers, H.; Sterk, H.: Some Tapas of Computer Algebra. Springer (1999).
48. Cojocaru, S.; Pfister, G.; Ufnarovski, V. (Eds.): Computational Commutative and Non-commutative Algebraic Geometry, NATO Science Series III, Computer and Systems Sciences 196 (2005)
49. Collins, G. E.; Mignotte, M.; Winkler, F.: Arithmetic in Basic Algebraic Domains. In: Buchberger, B.; Collins, G. E.; Loos, E. (eds.): Computer Algebra, Symbolic and Algebraic Computation, 2nd edn., 189-220. Springer (1983).
50. Corso, A.; Huneke, C.; Vasconcelos, W.: On the Integral Closure of Ideals. Manuscripta Math. 95, 331-347 (1998).
51. Coutinho, S. C.: A primer of algebraic D-modules. Cambridge Univ. Press (1995).
52. Cox, D.; Little, J.; O'Shea, D.: Ideals, Varieties and Algorithms. Springer (1992).
53. Cox, D.; Little, J.; O'Shea, D.: Using Algebraic Geometry. Springer (1998).
54. Czapor, S. R.: Solving Algebraic Equations. Combining Buchberger's Algorithm with Multivariate Factorization. J. Symb. Comp. 7, 49-53 (1989).
55. Davenport, J. H.; Siret, Y.; Tournier, E.: Computer Algebra, Systems and Algorithms for Algebraic Computation. Academic Press, London (1988).
56. Decker, W.; Greuel, G.-M.; de Jong, T.; Pfister, G.: The Normalization: a new Algorithm, Implementation and Comparisons. In: Proceedings EURO-CONFERENCE Computational Methods for Representations of Groups and Algebras (1.4. - 5.4.1997), Birkhäuser, 177-185 (1999).
57. Decker, W.; Greuel, G.-M.; Pfister, P.: Primary Decomposition: Algorithms and Comparisons. In: Algorithmic Algebra and Number Theory, Springer, 187-220 (1998).
58. Decker, W.; Lossen, Chr.: Computing in Algebraic Geometry; A quick start using Singular. Springer, (2006).
59. Dickenstein, A.; Emiris, I. Z.: Solving Polynomial Equations; Foundations, Algorithms, and Applications. Algorithms and Computations in Mathematics, Vol. 41, Springer, (2005).
60. Dixmier, J.: Enveloping Algebras. AMS (1996).
61. Dreyer, A: Primary Decomposition of Modules. Diplomarbeit, Kaiserslautern (2001).
62. Durfee, A. H.: Fifteen Characterizations of Rational Double Points and Simple Critical Points. Enseign. Math., II. Ser. 25, 132-163 (1979).
63. Duval, D.: Absolute Factorization of Polynomials: a Geometric Approach. SIAM J. Comput. 20, 1-21 (1991).
64. Ebert, G. L.: Some comments on the modular approach to Gröbner bases. ACM SIGSAM Bulletin 17, 28-32, (1983).
65. Eisenbud, D.: Homological Algebra on a Complete Intersection, with an Application to Group Representations. Transactions of the AMS 260(1), 35-64 (1980).
66. Eisenbud, D.: Commutative Algebra with a View toward Algebraic Geometry. Springer (1995).
67. Eisenbud, D.; Huneke, C.; Vasconcelos, W.: Direct Methods for Primary Decomposition. Invent. Math. 110, 207-235 (1992).
68. Eisenbud, D.; Grayson, D.; Stillman, M., Sturmfels, B.: Computations in Algebraic Geometry with Macaulay2. Springer, (2001).
69. Eisenbud, D.; Riemenschneider, O.; Schreyer, F.-O.: Resolutions of Cohen-Macaulay Algebras. Math. Ann. 257 (1981).
70. Eisenbud, D.; Robbiano, L.: Open Problems in Computational Algebraic Geometry and Commutative Algebra. In: Computational Algebraic Geometry and Commutative Algebra, Cortona 1991, Cambridge University Press 49-71 (1993).
71. Eisenbud, D.; Sturmfels, B.: Finding Sparse Regular Sequences. J. Pure Appl. Algebra 94, No. 2, 143-157 (1994).
72. 4). Journal of Pure and Applied Algebra 139, 61-88 (1999).
73. Faugère, C.; Gianni, P.; Lazard, D.; Mora, T.: Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering. J. Symb. Comp. 16, 329-344 (1993).
74. Fröberg, R.: An Introduction to Gröbner Bases. John Wiley & Sons, Chichester (1997).
75. Frühbis-Krüger, A.: Moduli Spaces for Space Curve Singularities. Dissertation, Kaiserslautern (2000).
76. Frühbis-Krüger, A.: Computing Moduli Spaces for Space Curve Singularities. JPAA 164, 165-178 (2001).
77. Frühbis-Krüger, A.: Partial Standard Bases for Families. Proc. of the ICMS (2002).
78. Frühbis-Krüger, A.; Pfister, G.: Some Applications of Resolution of Singularities from a Practical Point of View, Proceedings of the Conference Computational Commutative and Non-commutative Algebraic Geometry, Chisinau 2004, NATO Science Series III, Computer and Systems Sciences 196(2005), 104-117
79. Frühbis-Krüger, A.; Pfister, G.: Auflösung von Singularitäten, DMV-Mitteilungen 13-2(2005), 89-105
80. Frühbis-Krüger, A.; Pfister, G.: Algorithmic Resolution of Singularities, In: C. Lossen, G. Pfister: Singularities and Computer Algebra. LMS Lecture Notes 324, Cambridge University Press 157-184 (2006)
81. Frühbis-Krüger, A.; Terai, N.: Bounds for the Regularity of Monomial Ideals. LE Mathematiche, Vol. LIII, 83-97 (1998).
82. Fulton, W.: Intersection Theory. Springer (1984).
83. Galligo, A: Th́eorème de Division et Stabilit́e en Ǵeoḿetrie Analytique Locale. Ann. Inst. Fourier 29, 107-184 (1979).
84. von zur Gathen, J.; Gerhard, J.: Modern Computer Algebra. Cambridge University Press (1999).
85. Geddes, K. O.; Czapor, S. R.; Labahn, G.: Algorithms for Computer Algebra. Kluwer Academic Publishers Group. XVIII, 585 p., (1992).
86. Gelfand, I.; Kapranov, M.; Zelevinski, A.: Discriminants, Resultants and Multidimensional Determinants. Birkhäuser (1994).
87. Gerard, R.; Levelt, A. H. M.: Invariants Ḿesurant l'Irŕegularit́e en un Point Singulier des Systèmes d'Equations Diff́erentielles Lińeaires. Ann. Inst. Fourier, Grenoble 23(1), 157-195 (1973).
88. Gianni, P.: Properties of Gröbner Bases under Specialization. In: EURO-CAL'87, J. H. Davenport, Ed., Springer LNCS, Vol. 378, 293-297 (1989).
89. Gianni, P.; Miller, V.; Trager, B.: Decomposition of Algebras. ISSAC 88, Springer LNC 358, 300-308.
90. Gianni, P.; Trager, B.; Zacharias, G.: Gröbner Bases and Primary Decomposition of Polynomial Ideals. J. Symb. Comp. 6, 149-167 (1988).
91. Giovini, A.; Mora, T.; Niesi, G.; Robbiano, L., Traverso, C.: "One Sugar Cube, Please" or Selection Strategies in the Buchberger Algorithm. In: Proceedings Int. Symposium on Symbolic and Algebraic Computation ISSAC'91 (S. M. Watt ed.), ACM Press, New York, 49-54 (1991).
92. Giusti, M.: Some Effectivity Problems in Polynomial Ideal Theory. EU-ROSAM 84, Symbolic and Algebraic Computation. In: Proc. Int. Symp., Cambridge/Engl. 1984, Lecture Notes Comput. Sci. 174, 159-171 (1984).
93. Gordan, P.: Les Invariants des Formes Binaires. J. de Math. Pure et Appl. 6, 141-156 (1900).
94. Gräbe, H.-G.: The Tangent Cone Algorithm and Homogenization. Journal of Pure and Applied Algebra 97, 303-312 (1994).
95. Gräbe, H.-G.: Algorithms in Local Algebra. J. Symb. Comp. 19, 545-557 (1995).
96. Gräbe, H.: On lucky primes. Journal of Symbolic Computation 15, 199-209, (1994).
97. Grassmann, H.; Greuel, G.-M.; Martin, B.; Neumann, W.; Pfister, G.; Pohl, W.; Schönemann, H.; Siebert, T.: Standard Bases, Syzygies and their Implementation in Singular. In: Beiträge zur angewandten Analysis und Informatik, Shaker, Aachen, 69-96 (1994).
98. Grauert, H.: Uber die Deformation isolierter Singularitäten analytischer Mengen. Invent. Math. 15, 171-198 (1972).
99. Grauert, H.; Remmert, R.: Analytische Stellenalgebren. Grundl. 176, Springer (1971).
100. Gregory, R. T.; Krishnamurthy, E. V.: Methods and Applications of Errorfree Computations. Springer (1984).
101. Greuel, G.-M.: Deformation und Klassifikation von Singularitäten und Moduln. Jahresber. Deutsch. Math.-Verein. Jubiläumstagung 1990, 177-238 (1992).
102. Greuel, G.-M.: Applications of Computer Algebra to Algebraic Geometry, Singularity Theory and Symbolic-Numerical Solving. ECM 2000, Progress in Math. 202, 169-188, Birkhaüser Verlag (2001).
103. Greuel, G.-M.: Computer Algebra and Algebraic Geometry - Achievements and Perspectives. J. Symb. Comp. 30, 253-289 (2000).
104. Greuel, G.-M.: A Computer Algebra Solution to a Problem in Finite groups. Revista Matematica Iberoamericana 19, No. 2(2003), 413-424.
105. Greuel, G.-M.; Hertling, C.; Pfister, Gerhard: Moduli Spaces of Semiquasihomogeneous Singularities with fixed Principal Part. J. Algebraic Geometry 6, 169-199 (1997).
106. Greuel, G.-M.; Kröning, H.: Simple Singularities in Positive Characteristic. Math. Z. 203, 339-354 (1990).
107. Greuel, G.-M.; Lossen, C.; Schulze, M.: Three Algorithms in Algebraic Geometry, Coding Theory and Singularity Theory. In: C. Ciliberto et al (eds.), Applications of Algebraic Geometry to Coding Theory, Physics and Computation, Kluver (2001).
108. Greuel, G.-M.; Lossen, C.; Shustin, E.: Introduction to Singularities and Deformations. Springer (2006).
109. Greuel, G.-M.; Martin, B.; Pfister, G.: Numerische Charakterisierung quasihomogener Gorenstein-Kurvensingularitäten. Math. Nachr. 124, 123-131 (1985).
110. Greuel, G.-M.; Pfister, G.: Moduli for Singularities. In: Singularities London Math. Soc. LN 201, 119-146 (1991).
111. Greuel, G.-M.; Pfister, G.: Advances and Improvements in the Theory of Standard Bases and Syzygies. Arch. Math. 66, 163-196 (1996).
112. Greuel, G.-M.; Pfister, G.: Gröbner bases and Algebraic Geometry. In: Proceedings of the Conference 33 Years of Gröbner bases (Linz). Lecture Notes of London Math. Soc., 251, 109-143 (1998).
113. Greuel, G.-M.; Pfister, G.: Geometric Quotients of Unipotent Group Actions II. In: Singularities. The Brieskorn Anniversary Volume, 27-36, Progress in Mathematics 162, Birkhäuser (1998).
114. Greuel, G.-M.; Pfister, G.: Computer Algebra And Finite Groups, In Proceedings of the ICMS, Beijing 2002, 4-14.
115. Greuel, G.-M.; Pfister, G.: SINGULAR and Applications, Jahresbericht der DMV 108(4), 167-196, (2006).
116. Greuel, G.-M.; Pfister, G.; Schönemann, H.: Singular Reference Manual. Reports On Computer Algebra Number 12, May 1997, Centre for Computer Algebra, University of Kaiserslautern from www.singular.uni-kl.de.
117. Gröbner, W.: Uber die algebraischen Eigenschaften der Integrale von linearen Differentialgleichungen mit konstanten Koeffizienten. Monatsh. der Math. 47, 247-284 (1939).
118. Hardy, G. H.; Wright, E. M.: An Introduction to the Theory of Numbers. Oxford University Press (1954).
119. Harris, J.: Algebraic Geometry, A First Course. Springer (1992).
120. Hartshorne, R.: Algebraic Geometry, Vol. 52, Graduate Texts in Mathematics, New York, Springer (1977).
121. Hermann, G.: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Math. Annalen 95, 736-788 (1926).
122. Hillebrand, D.: Triangulierung nulldimensionaler Ideale - Implementierung und Vergleich zweier Algorithmen. Diplomarbeit, Dortmund (1999).
123. Hironaka, H.: Resolution of Singularities of an Algebraic Variety over a Field of Characteristic Zero. Ann. of Math. 79, 109-326 (1964).
124. Hirsch, T.: Die Berechnung des ganzen Abschlusses eines Ideals mit Hilfe seiner Rees-Algebra. Diplomarbeit, Kaiserslautern (2000).
125. Iglesias, A.; Takayama, N.: Mathematical Software - ICMS 2006. LNCS 4151.
126. Jansen, C.; Lux, K.; Parker, R.; Wilson, R.: An Atlas of Brauer Characters. Oxford University Press (1995).
127. De Jong, T.: An Algorithm for Computing the Integral Closure. J. Symb. Comp. 26, 273-277 (1999).
128. De Jong, T.; Pfister, G.: Local Analytic Geometry. Vieweg (2000).
129. Kalkbrener, M.: Algorithmic Properties of Polynomial Rings. J. Symb. Comp. 26, 525-581 (1998).
130. Kalkbrener, M.: Prime Decomposition of Radicals in Polynomial Rings. J. Symb. Comp. 18, 365-372 (1994).
131. Kandri-Rody, A.; Kapur, D.: Algorithms for Computing Gröbner Bases of Polynomial Ideals over Various Euclidean Rings. EUROSAM 84, Symbolic and Algebraic Computation, Proc. Int. Symp., Cambridge/Engl. 1984, Lecture Notes Comput. Sci. 174, 195-206 (1984).
132. Kandri-Rody, A.; Weispfenning, V.: Non-commutative Gröbner bases in algebras of solvable type. J. Symbolic Computation, 9(1):1-26 (1990)
133. Knuth, D. E.: The art of computer programming I (1997, 3rd ed.), II (1997, 3rd ed.), III (1998, 3rd ed.), Addison-Wesley.
134. Kornerup, P.; Gregory, R.: Mapping integers and Hensel codes onto Farey fractions. Bit 23, 9-20, (1983).
135. Kredel, H.: Solvable polynomial rings. Shaker (1993).
136. Kredel, H.; Weispfenning, V.: Computing Dimension and Independent Sets for Polynomial Ideals. J. Symb. Comp. 6, 231-248 (1988).
137. Kreuzer, M.; Robbiano, L.: Computational Commutative Algebra 1. Springer (2000).
138. Kreuzer, M.; Robbiano, L.: Computational Commutative Algebra 2. Springer (2005).
139. Krick, T.; Logar, A.: An Algorithm for the Computation of the Radical of an Ideal in the Ring of Polynomials. AAECC9, Springer LNCS 539, 195-205 (1991).
140. Krüger, K.: Klassifikation von Hyperflächensingularitäten. Diplomarbeit, Kaiserslautern (1997).
141. Kunz, E.: Einführung in die kommutative Algebra und algebraische Geometrie. Vieweg (1980). English Translation: Introduction to Commutative Algebra and Algebraic Geometry. Birkhäuser (1985).
142. Kurke, H.; Mostowski, T.; Pfister, G.; Popescu, D.; Roczen, M.: Die Approximationseigenschaft lokaler Ringe. SLN 634, Springer (1978).
143. Kurke, H.; Pfister, G.; Roczen, M.: Henselsche Ringe und algebraische Geometrie. Berlin (1975).
144. Lang, S.: Algebra. Addison-Wesley (1970).
145. Laudal, O. A.: Formal Moduli of Algebraic Structures. SLN 754, Springer (1979).
146. Laudal, O. A.; Pfister G.: Local moduli and singularities. SLN 1310, Springer (1988).
147. Lazard, D.: A new Method for Solving Algebraic Systems of Positive Dimension. Discr. Appl. Math. 33, 147-160 (1991).
148. Lazard, D.: Gröbner Bases, Gaussian Elimination and Resolution of Systems of Algebraic Equations. Proceedings of EUROCAL 83, Lecture Notes in Computer Science 162, 146-156 (1983).
149. Lazard, D.: Solving Zero-dimensional Algebraic Systems. J. Symb. Comp. 13, 117-131 (1992).
150. Lecerf, G.; A quick Implementation of the Absolute Factorization, preprint (2006).
151. Lenstra, A. K.; Lenstra, H. W. Jr.; Lovász, L.: Factoring Polynomials with Rational Coefficients. Math. Ann. 261, 515-534 (1982).
152. Levandovskyy, V.: Non-commutative computer algebra for polynomial algebras: Gröbner bases, applications and implementation. Doctoral Thesis, Universität Kaiserslautern (2005). Available from: http://kluedo.ub-unikl. de/volltexte/2005/1883/.
153. Levandovskyy, V.: PBW Bases, Non-Degenerate Conditions and Applications. In: Buchweitz, R.-O.; Lenzing, H. (eds.): Representation of algebras and related topics. Proceedings of the ICRA X conference, Vol. 45, 229-246. AMS. Fields Institute Communications (2005).
154. Li, H.: Noncommutative Gröbner bases and filtered-graded transfer. Springer (2002).
155. Lossen, C.; Pfister, G. (Eds.): Singularities and Computer Algebra. LMS Lecture Notes 324, Cambridge University Press (2006)
156. Lossen, C.; Pfister, G.: Aspects of Gert-Martin Greuel's Mathematical Work. In: C. Lossen, G. Pfister: Singularities and Computer Algebra. LMS Lecture Notes 324, Cambridge University Press (2006), xvii-xxxvi
157. Macaulay, F. S.: Some Properties of Enumeration in the Theory of Modular Systems. In: Proc. London Math. Soc. 26, 531-555 (1939).
158. Martin, B.: Computing Versal Deformations with Singular. In: Algorithmic Algebra and Number Theory, Springer, 283-294 (1998).
159. Matsumura, H.: Commutative Ring Theory. Cambridge Studies in Advanced Math. 8 (1986).
160. Matsumura, H.: Commutative Algebra (second edition). Mathematical Lecture Notes Series, Benjamin (1980).
161. Mayr, E. W.; Meyer, A. R.: The Complexity of the Word Problem for Commutative Semigroups and Polynomial Ideals. Adv. Math. 46, 305-329 (1982).
162. Mignotte, M.: Mathematics for Computer Algebra. Springer (1991).
163. Miller, Ezra; Sturmfels, Bernd: Cobinatorial Commutative Algebra. Graduate Texts in Mathematics 227, Springer (2005).
164. Milnor, T.: Singular Points of Complex Hypersurfaces. Ann. of Math. Studies 61, Princeton (1968).
165. Mines, R.; Richman, F.; Reitenburg, W.: A Course in Constructive Algebra. Springer, New York (1988).
166. Miola, A.; Mora, T.: Constructive Lifting in Graded Structures: A Unified View of Buchberger and Hensel Methods. J. Symb. Comp. 6, 305-322 (1988).
167. Mishra, B.: Algorithmic Algebra. Springer (1993).
168. Möller, H. M.: On the Construction of Gröbner Bases using Syzygies. J. Symb. Comp. 6, 345-360 (1988).
169. Möller, H. M.: On Decomposing Systems of Polynomial Equations with Finitely many Solutions. Appl. Algebra Eng. Commun. Comput. 4, 217-230 (1993).
170. Möller, H. M.: Solving of Algebraic Equations - an Interplay of Symbolical and Numerical Methods. Multivariate Approximation, Recent Trends and Results, Akademie Verlag, 161-176 (1997).
171. Möller, H. M.: Gröbner Bases and Numerical Analysis. In: B. Buchberger and F. Winkler (Eds.): Gröbner Bases and Applications. Cambridge University Press, LNS 251, 159-178 (1998).
172. Motsak, O.: Computation of the central elements and centralizers of sets of elements in non-commutative polynomial algebras. Diploma thesis, Kaiserslautern 2006.
173. Möller, H. M.; Mora, T.: Upper and Lower Bounds for the Degree of Gröbner Bases. In: EUROSAM 84, J. Fitch Ed., Springer LNCS, Vol. 174, 172-183 (1984).
174. Möller, H. M.; Mora, T.: New Constructive Methods in Classical Ideal Theory. J. Algebra 100, 138-178 (1986).
175. Möller, H. M.; Mora, T.: Computational Aspects of Reduction Strategies to Construct Resolutions of Monomial Ideals. In: Proceedings AAECC 2, Lecture Notes in Comput. Sci. 228 (1986).
176. Mora, T.: An Algorithm to Compute the Equations of Tangent Cones. In: Proceedings EUROCAM 82, Lecture Notes in Comput. Sci. (1982).
177. Mora, T.: La Queste del Saint Graal: A Computational Approach to Local Algebra. Discrete Applied Math. 33, 161-190 (1991).
178. Mora, T.: Gröbner Bases in non-commutative Algebras. In: Proc. of the Internatinal Symposium on Symbolic and Algebraic Computation (ISSAC'88), 150-161, LNCS 358 (1989).
179. Mora, T.; Pfister, G.; Traverso, C.: An Introduction to the Tangent Cone Algorithm. In: Issues in non-linear geometry and robotics, JAI Press (6), 199-270 (1992).
180. Mora, T.; Robbiano, L.: The Gröbner Fan of an Ideal. J. Symb. Comp. 6, 183-208 (1988).
181. Mumford, D.: Algebraic Geometry I, Complex Projective Varieties. Springer (1976).
182. Mumford, D.: The Red Book of Varieties and Schemes. LNM 1358, Springer (1989).
183. Nagata, M.: Local Rings. Wiley (1962).
184. O'Caroll, L.; Flenner, H.; Vogel, W.: Joins and Intersections. Springer (1999).
185. Pauer, F.: On lucky ideals for Gröbner bases computations. Journal of Symbolic Computation 14, 471-482, (1992).
186. Peskine, C.: An Algebraic Introduction to Complex Projective Geometry I. Commutative Algebra. Cambridge studies in advanced mathematics 47 (1996).
187. Pfister, G.: The Tangent Cone Algorithm and some Applications to Algebraic Geometry. Proc. of the MEGA Conference 1990. Birkhäuser Vol. 94, 401-409 (1991).
188. Pfister, G.: A Problem in Group Theory Solved by Computer Algebra, In Proceedings of the Conference Commutative Algebra, Singularities and Computer Algebra, Sinaia 2002, Kluwer Academic Publishers 2003, 217-223.
189. Pfister, G.: On Modular Computation of Standard Basis, to appear in Analele Stiintific e ale Univ. Ovidius, Mathematical Series, (2007).
190. Pfister, G.; Schönemann, H.: Singularities with exact Poincarè Complex but not Quasihomogeneous. Revista Mathematica Madrid (2) 2 y 3, 161-171 (1989).
191. Radu, N.: Inele Locale. Bucharest (1968).
192. Ŕedei, L.: Algebra, Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig (1959)
193. Renschuch, B.: Elementare und praktische Idealtheorie. Berlin (1979).
194. Ritt, J. F.: Differential equations from the algebraic standpoint. Colloquium Publications XIV, AMS, (1932).
195. Ritt, J. F.: Differential algebra. Colloquium Publications XXXIII, AMS, (1950).
196. Robbiano, L.: Term Orderings on the Polynomial Ring. In: Proceedings EUROCAL 85, Lecture Notes in Computer Science 204, Springer (1985).
197. Robbiano, L.: On the Theory of Graded Structures. J. Symb. Comp. 2, 139-170 (1986).
198. Robbiano, L.; Sweedler, M.: Subalgebra Bases. In: Commutative Algebra, Proceedings Workshop, Salvador/Brazil 1988, Lecture Notes in Math., Vol. 1430, 61-87, Springer (1990).
199. Saito, M.; Sturmfels, B., Takayama, N.: Gröbner Deformations of Hypergeometric Differential Equations. Springer (2000).
200. Sasaki, T.; Takeshima, T.: A modular method for Gröbner-basis construction over ℚ and solving system of algebraic equations. Journal of Information Processing 12, 371-379, (1989).
201. Scheja, G.; Storch, U.: Lehrbuch der Algebra Teil 1 und 2. B. G. Teubner, Stuttgart (1988).
202. Schmidt, J.: Algorithmen zur Berechnung größter gemeinsamer Teiler im univariaten Polynomring über den ganzen Zahlen und deren effiziente Implementierung in Factory. Diplomarbeit, Kaiserslautern (1999).
203. Schreyer, F.-O.: Die Berechnung von Syzygien mit dem verallgemeinerten Weierstrasschen Divisionssatz. Diplomarbeit, Hamburg (1980).
204. Schreyer. F.-O.: A Standard Basis Approach to Syzygies of Canonical Curves. J. Reine Angew. Math., 421, 83-123 (1991).
205. Schreyer, F.-O.: Syzygies of Canonical Curves and Special Linear Series. Math. Ann., 275 (1986).
206. Schulze, M.: Computation of the Monodromy of an Isolated Hypersurface Singularity. Diploma Thesis, Kaiserslautern (1999).
207. Schulze, M.: Algorithms for the Gauss-Manin Connection. J. Symb. Comp. 32, 549-564 (2001).
208. Schulze, M.: Algorithmic Gauss-Manin Connection. Algorithms to Compute Hodge-theoretic Invariants of Isolated Hypersurface Singularities. Dissertation, Kaiserslautern (2002).
209. Seidenberg, A.: Constructions in Algebra. Trans. Amer. Math. Soc. 197, 273-313 (1974).
210. Seidenberg, A.: Construction of the Integral Closure of a Finite Integral Domain II. vProceedings Amer. Math. Soc. 52, 368-372 (1975).
211. Serre, J.-P.: Algèbre locale multiplicit́es. SLN 11, Springer (1975).
212. Shannon, D.; Sweedler, M.: Using Gröbner Bases to Determine Algebra Membership, Split Surjective Algebra Homomorphisms Determine Birational Equivalence. J. Symb. Comp. 6, 267-273 (1988).
213. Shimoyama, T.; Yokoyama, K.: Localization and Primary Decomposition of Polynomial ideals. J. Symb. Comp. 22, 247-277 (1996).
214. Stillman, M.; Tsai, H.: Using SAGBI Bases to Compute Invariants. Journal of Pure and Applied Algebra 139, 285-302 (1999).
215. Stobbe, R.: Darstellung algebraischer Kurven mittels Computergraphik. Diplomarbeit, Kaiserslautern (1992).
216. Stolzenberg, G.: Constructive Normalization of an Algebraic Variety. Bull. AMS., 74, 595-599 (1968).
217. Sturmfels, B.: Algorithms in Invariant Theory. In: Texts and Monographs in Symbolic Computation. Springer (1993).
218. Sturmfels, B.: Gröbner Bases and Convex Polytopes. AMS University Lecture Series 8 (1995).
219. Traverso, C.: Hilbert functions and the Buchberger algorithm. J. Symb. Comp. 22, No. 4, 355-376 (1996).
220. Trinks, W.: Uber B. Buchbergers Verfahren, Systeme algebraischer Gleichungen zu lösen. J. Number Theory, 10, 475-488 (1978).
221. Valentine, F. A: Convex Sets. Krieger (1976).
222. Vasconcelos, W. V.: Arithmetic of Blowup Algebras. Lecture Note 195, Cambridge University Press (1994).
223. Vasconcelos, W. V.: Computational Methods in Commutative Algebra and Algebraic Geometry. Springer (1998).
224. Wall, C. T. C.: Classification of Unimodal Isolated Singularities of Complete Intersections. In: Singularities, Arcata 1981 (Ed. Orlik, P.), Proceedings Sympos. Pure Math. 40(2), 625-640 (1983).
225. Wang, D.: Irreducible Decomposition of Algebraic Varieties via Characteristic Sets and Gröbner Bases. Computer aided Geometric Design 9, 471-484 (1992).
226. Wang, D.: Decomposing Polynomial Systems into Simple Systems. J. Symb. Comp. 25, 295-314 (1998).
227. Wang, D.: Computing Triangular Systems and Regular Systems. J. Symb. Comp. 30, 221-236 (2000).
228. Wang, D.: Elimination Methods. In: Texts and Monographs in Symbolic Computation. Springer (2001).
229. Wang, P. S.: An Improved Multivariate Polynomial Factorizing Algorithm, Math. Comp. 32, 1215-1231 (1978)
230. Wang, P. S.: The EEZ-GCD Algorithm, ACM SIGSAM Bull. 14, 50-60 (1980)
231. Weispfenning, V.: Constructing Universal Gröbner Bases. Applied Algebra, Algebraic Algorithms and Error-correcting Codes, Proc. 5th Int. Conference, AAECC-5, Menorca, Spain, 1987, Lect. Notes Comput. Sci. 356, 408-417 (1989).
232. Weispfenning, V.: Comprehensive Gröbner Bases. J. Symb. Comp. 14, 1-29 (1992).
233. Wichmann, T.: der FGLM-Algorithmus: verallgemeinert und implementiert in SINGULAR. Diplomarbeit, Kaiserslautern (1997).
234. Winkler, F.: A p-adic approach to the computation of Gröbner bases. Journal of Symbolic Computation 6, 287-304, (1987).
235. Winkler, F.: Polynomial Algorithms in Computer Algebra. In: Texts and Monographs in Symbolic Computation. Springer (1996).
236. Wu, W. T.: Basic Principles of Mechanical Theorem Proving in Elementary Geometries. J. of System Science and Mathematical Science, 4(3), 207-235 (1984).
237. Yoshino, Y.: Cohen-Macaulay Modules over Cohen-Macaulay Rings. Cambridge University Press (1990).
238. Zariski, O.; Samuel, P.: Commutative Algebra. Vol. I, II, Springer (1960).
239. ASIR (Noro, M.; Shimoyama, T.; Takeshima, T.): http://www.asir.org/.
240. CoCoA (Robbiano, L.): A System for Computation in Algebraic Geometry and Commutative Algebra. Available from cocoa.dima.unige.it/cocoa
241. Macaulay (Bayer, D.; Stillman, M.): A System for Computation in Algebraic Geometry and Commutative Algebra. Available via ftp from zariski.harvard.edu.
242. Macaulay 2 (Grayson, D.; Stillman, M.): A Computer Software System Designed to Support Research in Commutative Algebra and Algebraic Geometry. Available from http://math.uiuc.edu/Macaulay2.
243. Macsyma (Macsyma Inc.): http://www.scientek.com/macsyma/main.htm
244. Magma (Computational Algebra Group within School of Maths and Statistics of University of Sydney): http://magma.maths.usyd.edu.au/magma
245. Maple (Waterloo Maple Inc.): http://www.maplesoft.com/.
246. MATHEMATICA (Wolfram Research Inc.): http://www.wolfram.com/.
247. MuPAD (MuPAD Research Group and Sciface Software GmbH & Co. KG): http:/www.mupad.de/.
248. Reduce: http://www.uni-koeln. de/REDUCE.
249. SAGE (Mathematics Software (Verson 2.7), (Stein, W.): http://www.sagemath.org
250. SINGULAR (Greuel, G.-M.; Pfister, G.; Schönemann, H.): A Computer Algebra System for Polynomial Computations. Centre for Computer Algebra, University of Kaiserslautern, free software under the GNU General Public Licence (1990-2007). http://www.singular.uni-kl.de.