Triangular Matrix Representations

Journal of Algebra

Volumn 230, Issue 2, 2000, Pages 558-595

  Birkenmeier, Gary F ^a   Heatherly, Henry E ^a   Kim, Jin Yong ^b   Park, Jae Keol ^c  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

^b Kyung Hee University   (South Korea)

^c Pusan National University   (South Korea)

Author keywords

Canonical form; Generalized triangular matrix representation; Global dimension; Piecewise domain; Piecewise prime ring; Quasi Baer ring; Semicentral idempotent

Indexed keywords

EID: 0034662520     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.2000.8328     Document Type: Article

References (46)

1. Anderson F. W., Fuller K. R. Rings and Categories of Modules. 1992;Springer-Verlag, Heidelberg/New York.
2. Auslander M. On the dimension of modules and algebras, III. Nagoya Math. J. 9:1955;67-77.
3. Azumaya G. On maximal central algebras. Nagoya Math. J. 2:1951;119-150.
4. Birkenmeier G. F., Heatherley H. E., Lee E. K. Completely prime ideals and associated radicals. Jain S. K., Rizvi S. Tariq, . Ring Theory. 1993;102-129 World Scientific, Singapore.
5. G. F. Birkenmeier, A Decomposition Theory of Rings, Ph.D. Thesis, University of Wisconsin at Milwaukee, Milwaukee, WI, 1975.
6. Birkenmeier G. F. Indecomposable decompositions and the minimal direct summand containing the nilpotents. Proc. Amer. Math. Soc. 73:1979;11-14.
7. Birkenmeier G. F. Baer rings and quasi-continuous rings have a MDSN. Pacific J. Math. 97:1981;283-292.
8. Birkenmeier G. F. Idempotents and completely semiprime ideals. Comm. Algebra. 11:1983;567-580.
9. Barthwal S., Jain S. K., Kanwar P., Lopez-Permouth S. R. Nonsingular semiperfect CS-rings. J. Algebra. 203:1998;361-373.
10. Chase S. U. A generalization of the ring of triangular matrices. Nagoya Math. J. 18:1961;13-25.
11. Chatters A. W., Hajarnavis C. R. Rings in which every complement right ideal is a direct summand. Quart. J. Math. Oxford Ser. (2). 28:1977;61-81.
12. Chatters A. W., Hajarnavis C. R. Rings with Chain Conditions. 1980;Pitman, Boston.
13. Chatters A. W., Khuri S. M. Endomorphism rings of modules over non-singular CS rings. J. London Math. Soc. (2). 21:1980;434-444.
14. Clark W. E. Twisted matrix units semigroup algebras. Duke Math. J. 34:1967;417-423.
15. Chari V., Pressley A. A Guide to Quantum Groups. 1994;Cambridge Univ. Press, Cambridge.
16. Faith C. Semiperfect Prüfer rings and FPF rings. Israel J. Math. 26:1977;166-177.
17. Faith C. Injective quotient rings of commutative rings. Module Theory. Lecture Notes in Math. 700:1979;Springer-Verlag, Heidelberg/New York. p. 151-203.
18. Fields K. L. On the global dimension of residue rings. Pacific J. Math. 32:1970;345-349.
19. Gordon R., Robson J. C. Krull dimension. Mem. Amer. Math. Soc. 133:1973.
20. Gordon R., Small L. W. Piecewise domains. J. Algebra. 23:1972;553-564.
21. Harada M. Hereditary semi-primary rings and triangular matrix rings. Nagoya Math. J. 27:1966;463-484.
22. Hudson T. D., Katsoulis E. G., Larson D. R. Extreme points in triangular UHF algebras. Trans. Amer. Math. Soc. 349:1997;3391-3400.
23. Jacobson N. Structure of Rings. Amer. Math. Soc. Colloq. Publ. 37:1964;Amer. Math. Soc. Providence.
24. Kaplansky I. Rings of Operators. 1968;Benjamin, New York.
25. Krause G. On the Krull-dimension of left Noetherian left Matlis-rings. Math. Z. 118:1970;207-214.
26. Kelarev A. V., Van der Merwe A. B., van Wyk L. The minimum number of idempotent generators of an upper triangular matrix algebra. J. Algebra. 205:1998;605-616.
27. Lam T. Y. A First Course in Noncommutative Rings. 1991;Springer-Verlag, Heidelberg/New York.
28. Lam T. Y. A lifting theorem, and rings with isomorphic matrix rings. Chan K. Y., Liu M. C., Five Decades as a Mathematician and Educator: On the 80th Birthday of Professor Y. C. Wong. 1995;169-186 World Scientific, Singapore.
29. Lam T. Y. Modules with isomorphic multiples and rings with isomorphic matrix rings - A survey. PAM. 736:1998;University of California at Berkeley.
30. Lam T. Y. Lectures on Modules and Rings. 1999;Springer-Verlag, Heidelberg/New York.
31. Lawrence J. A singular primitive ring. Proc. Amer. Math. Soc. 45:1974;59-62.
32. Levy L. Torsion-free and divisible modules over non-integral-domains. Canad. J. Math. 15:1963;132-151.
33. Li M. S., Zelmanowitz J. M. Artinian rings with restricted primeness conditions. J. Algebra. 124:1989;139-148.
34. Michler G. O. Structure of semi-perfect hereditary Noetherian rings. J. Algebra. 13:1969;327-344.
35. Moody R. V., Pianzola A. Lie Algebras with Triangular Decompositions. 1995;Wiley, New York.
36. Nicholson W. K. Semiregular modules and rings. Canad. J. Math. 28:1976;1105-1120.
37. Nǎstǎsescu C., van Oystaeyen F. Dimensions of Ring Theory. 1987;Reidel, Dordrecht/Boston.
38. Paterson A. L. T., Smith R. R. Higher-dimensional virtual diagonals and ideal cohomology for triangular algebras. Trans. Amer. Math. Soc. 349:1997;1919-1943.
39. Pollingher A., Zaks A. On Baer and quasi-Baer rings. Duke Math. J. 37:1970;127-138.
40. Rowen L. Ring Theory. 1988;Academic Press, Boston.
41. Small L. W. Semihereditary rings. Bull. Amer. Math. Soc. 73:1967;656-658.
42. 1. J. Algebra. 73:1981;552-555.
43. Stenström B. Rings of Quotients. 1975;Springer-Verlag, Heidelberg/New York.
44. Smith K. C., van Wyk L. An internal characterization of structural matrix rings. Comm. Algebra. 33:1994;5599-5622.
45. Wheeler W. H. Model theory of strictly upper triangular matrix rings. J. Symbolic Logic. 45:1980;455-463.
46. Wisbauer R. Foundations of Module and Ring Theory. 1991;Gordon & Breach, Philadelphia.