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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A characterization of Artinian rings whose endomorphism rings have finite global dimension


Author: Dan Zacharia
Journal: Proc. Amer. Math. Soc. 104 (1988), 37-38
MSC: Primary 16A35; Secondary 16A60
MathSciNet review: 958038
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if $ \Lambda $ is a left artinian ring having the property that for every idempotent $ e$, the ring $ e\Lambda e$ has finite global dimension then $ \Lambda $ is a quotient of an hereditary artinian ring.


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

  • [1] Edward L. Green, Remarks on projective resolutions, Representation theory, II (Proc. Second Internat. Conf., Carleton Univ., Ottawa, Ont., 1979), Lecture Notes in Math., vol. 832, Springer, Berlin, 1980, pp. 259–279. MR 607158 (82b:16024)
  • [2] J. P. Jans and Tadasi Nakayama, On the dimension of modules and algebras. VII. Algebras with finite-dimensional residue-algebras, Nagoya Math. J. 11 (1957), 67–76. MR 0086824 (19,250a)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0958038-6
PII: S 0002-9939(1988)0958038-6
Article copyright: © Copyright 1988 American Mathematical Society