Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Algebras of finite self-injective dimension


Author: Mitsuo Hoshino
Journal: Proc. Amer. Math. Soc. 112 (1991), 619-622
MSC: Primary 16P20; Secondary 16E10
DOI: https://doi.org/10.1090/S0002-9939-1991-1047011-8
MathSciNet review: 1047011
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ A$ be an artin algebra. Then $ A$ has finite self-injective dimensions on both sides if and only if every finitely generated left $ A$-module has finite Gorenstein dimension.


References [Enhancements On Off] (What's this?)

  • [1] M. Auslander, Coherent functors, Proc. Conf. Cat. Algebra, Springer, Berlin, 1966, pp. 189-231. MR 0212070 (35:2945)
  • [2] M. Auslander and M. Bridger, Stable module theory, Mem. Amer Math. Soc., no. 94, Amer. Math. Soc., Providence, RI, 1969. MR 0269685 (42:4580)
  • [3] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, 1956. MR 0077480 (17:1040e)
  • [4] A. Zaks, Injective dimension of semiprimary rings, J. Algebra 13 (1969), 73-86. MR 0244325 (39:5640)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16P20, 16E10

Retrieve articles in all journals with MSC: 16P20, 16E10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1047011-8
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society