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Proceedings of the American Mathematical Society

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

 

 

Correspondence theorems for nondegenerate modules and their endomorphism rings


Author: Zheng Ping Zhou
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1994-1211594-8
Article copyright: © Copyright 1994 American Mathematical Society