Virtual topology and functor geometry

Virtual Topology and Functor Geometry

Volumn , Issue , 2007, Pages 1-151

  Van Oystaeyen, Fred ^a  

^a UNIVERSITY OF ANTWERP   (Belgium)

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[No Author keywords available]

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EID: 85055491873     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/9781420060577     Document Type: Book

References (53)

1. Aly, F. S., and F. Van Oystaeyen. “Hopf Filtrations and Larsson-Type Orders in Hopf Algebras.” J. of Algebra 267(2003): 756–772.
2. Artin, M. “Grothendieck Topologies.” Cambridge, MA: Harvard Univ. Lecture Notes, 1962.
3. Artin, M., A. Grothendieck, and J.-L. Verdier. “Théorie des topos et cohomologie étale des schémas.” Lect. Notes in Math. 269, 270, 305, Berlin: Springer Verlag, 1972–73.
4. Artin, M., and J. Zhang, “Noncommutative Projective Schemes,” Adv. in Math. 109 (1994): 228–287.
5. Asensio, M.-J., M. Van den Bergh, and F. Van Oystaeyen. “A New Algebraic Approach to Microlocalization of Filtered Rings.” Trans. Amer. Math. Soc. 316, no. 2(1989): 537–555.
6. G. Birkhoff. Lattice Theory, AMS Colloquium Publ. XXV, 1940, reprint edition 1967.
7. T. S. Blyth. Lattices and Ordered Algebraic Structures. London: Springer Verlag, 2005.
8. ∗-Algèbres et Géometrie Différentielle.” C. R. Acad. Sc. Paris 290 (1980): 599–604.
9. Connes, A., and Michel Dubois-Violette. “Noncommutative Finitedimensional Manifolds. I. Spherical Manifolds and Related Examples.” Notes IHES/M/01/32, juillet 2001.
10. Gabriel, P. “Des catégories abéliennes.” Bull. Soc. Math. France 90 (1962): 323–448.
11. Gabriel, P., and R. Rentschler. “Sur la dimension des anneaux et ensembles ordonnées.” C. R. Acad. Sci. Paris 265(1967): 712–715.
12. Godement, R. Théorie des faisceaux. Paris: Hermann, 1958.
13. Golan, J. Localization of Noncommutative Rings. New York: Marcel Dekker, 1975.
14. Golan, J., J. Raynand, and F. Van Oystaeyen. “Sheaves over the Spectra of Certain Noncommutative Rings.” Comm. Algebra, 4(1976): 491–502.
15. Goldblatt, R. Topoi. The Categorical Analysis of Logic, 2nd ed. Studies in Logic and the Foundations of Mathematics 98. Amsterdam: North-Holland Publishing Company, 1984, xvi.
16. Goldman, O. “Rings and Modules of Quotients.” J. of Algebra 13(1969): 10–47.
17. Grothendieck, A. “Produits tensoriels topologiques et espaces nucléaires.” Memoirs Am. Math. Soc. 16, 1955.
18. Joyal, A., and R. Street. “Braided Monoidal Categories.” Adv. in Mathematics 102(1993): 20–78.
19. Kassel, C. Quantum Groups. Berlin: Springer Verlag, 1995.
20. Lambek, J. Torsion Theories, Additive Semantics and Rings of Quotients, LNM 197. Berlin: Springer Verlag, 1971.
21. Lambek, J. “Noncommutative Localization.” Bull. Am. Math. Soc. 79(1973): 857–872.
22. Lambek, J., and B. Rattray. “Localization and Duality in Additive Categories.” Houston J. of Math. 1(1975): 87–106.
23. Lambek, J. “Localization at Epimorphisms and Quasi-injectives.” J. of Algebra 38(1976): 163–181.
24. Le Bruyn, L., and F. Van Oystaeyen. “Quantum Sections and Gauge Algebras.” Publ. Math. 36 (2A)(1992): 693–714.
25. Le Bruyn, L., M. Van den Bergh, and F. Van Oystaeyen. Graded Orders, Boston: Birkhauser Verlag, 1988.
26. Li, H., and F. Van Oystaeyen. “Zariskian Filtrations.” Comm. Alg. 17(1989): 2945–2970.
27. Li, H., and F. Van Oystaeyen. “Zariskian Filtrations.” Kluwer Monographs, Vol. 2. Boston: Kluwer Academic Press, 1995.
28. McLane, S. Categories for the Working Mathematician. New York: Springer Verlag, 1974.
29. Manin, Yu. Quantum Groups and Noncommutative Geometry. Montreal: Publ. Centre Math., 1988.
30. Murdoch, D., and F. Van Oystaeyen. “Noncommutative Localization and Sheaves.” J. of Algebra 35 (1975): 500–525.
31. Nǎstǎsescu, C., and F. Van Oystaeyen. Graded and Filtered Rings and Modules, LNM 758. Berlin: Springer Verlag, 1979.
32. Nǎstǎsescu, C., and F. Van Oystaeyen. Graded Ring Theory, Math. Library. Vol. 28. North Holland, Amsterdem, 1982.
33. Nǎstǎsescu, C., and F. Van Oystaeyen. Dimensions of Ring Theory. Boston: D. Reidel Publ. Co., 1987.
34. Nǎstǎsescu, C., M. Van den Bergh, and F. Van Oystaeyen. “Separable Functors Applied to Graded Ring Theory.” J. of Algebra 123 (1989): 397–413.
35. Nwabueze, K. K., and F. Van Oystaeyen. “Presheaves over Lattices. Application to Twisted Limits of Finite Groups.” Comm. Alg. 25(3) (1997): 887–903.
36. Popescu, N. Abelian Categories with Applications to Rings and Modules. London: Academic Press, 1973.
37. Procesi, C. Rings with Polynomial Identities. New York: Marcel Dekker, 1977.
38. Radwan, A., and F. Van Oystaeyen. Microstructure Sheaves and Quantum Sections over Projective Schemes, Paris: Hermann, 1995.
39. Rafael, M. D., Separable Functors Revisited, Comm. Algebra, 18, 1990, Vol. 5, 1445–1459.
40. Sallam, R., and F. Van Oystaeyen. “A Microstructure Sheaf and Quantum Section over a Projective Scheme.” J. of Algebra 158, no. 1 (1993): 201–225.
41. Serre, J.-P. “Faisceaux Algébriques Cohérents.” Ann. Math. 61 (1955): 197–278.
42. Stenström, B. Rings of Quotients. Berlin: Springer Verlag, 1975.
43. Tennison, B. R. Sheaf Theory, LMS Lect. Notes Vol. 20. Cambridge: Cambridge Univ. Press, 1975.
44. Van Oystaeyen, F. Prime Spectra in Noncommutative Algebra, LNM 444, Berlin: Springer Verlag, 1975.
45. Van Oystaeyen, F. “Compatibility of Kernel Functors and Localization Functors.” Bull. Soc. Math. Belg. XVIII (1976): 131–137.
46. Van Oystaeyen, F. Algebraic Geometry for Associative Algebras. Math. Monographs Vol. 232, New York: M. Dekker, 2000.
47. Van Oystaeyen, F., and A. Verschoren. Noncommutative Algebraic Geometry, LNM 887. Berlin: Springer Verlag, 1981.
48. Van Oystaeyen, F., and A. Verschoren. Reflectors and Localization, Applications to Sheaf Theory, Lect. Notes Vol. 41. New York: M. Dekker, 1978.
49. Van Oystaeyen, F., and L. Willaert. “Grothendieck Topology, Coherent Sheaves and Serre’s Theorem for Schematic Algebras.” J. Pure Applied Algebra 104 (1995): 109–122.
50. Van Oystaeyen, F., and L. Willaert. “Cohomology of Schematic Algebras.” J. of Algebra 183, 2 (1996): 359–364.
51. Van Oystaeyen, F., and L. Willaert, “Examples and Quantum Sections of Schematic Algebras.” J. Pure Applied Algebra 120 (1997): 195–211.
52. Yetter, D. N. “Quantum Groups and Representations of Monoidal Categories.” Math. Proc. Cambridge Phil. Soc. 108 (1990): 261–290.
53. Zariski, O. Algebraic Sheaf Theory. Sunrise, FL: AMS, 1956, 117–141.