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