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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Correspondence theorems for nondegenerate modules and their endomorphism rings
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by Zheng Ping Zhou PDF
Proc. Amer. Math. Soc. 121 (1994), 25-32 Request permission

Abstract:

Let $_RU$ be a left R-module whose Morita context is nondegenerate and $S = {\text {End}}(U)$. We show the following: (1) There is a projectivity (that is, an order-preserving bijection) between the complement submodules of $_RU$ and the complement left ideals of S; (2) S is a left CS ring if and only if $_RU$ is a CS module; (3) S is a Baer and left CS ring if and only if $_RU$ is a nonsingular and CS module. Special cases include some earlier works.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 25-32
  • MSC: Primary 16S50
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1211594-8
  • MathSciNet review: 1211594