Correspondence theorems for nondegenerate modules and their endomorphism rings

Zhou, Zheng Ping

doi:10.1090/S0002-9939-1994-1211594-8

Correspondence theorems for nondegenerate modules and their endomorphism rings
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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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