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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of Artinian rings whose endomorphism rings have finite global dimension
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by Dan Zacharia PDF
Proc. Amer. Math. Soc. 104 (1988), 37-38 Request permission

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
  • 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
  • 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 86824
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 104 (1988), 37-38
  • MSC: Primary 16A35; Secondary 16A60
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0958038-6
  • MathSciNet review: 958038