Properties of endomorphism rings of modules and their duals
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- by Soumaya Makdissi Khuri PDF
- Proc. Amer. Math. Soc. 96 (1986), 553-559 Request permission
Abstract:
Let $_RM$ be a nonsingular left $R$-module whose Morita context is nondegenerate, let $B = \operatorname {End}_{R}M$ and let ${M^ * } = \operatorname {Hom}_{R}(M,R)$. We show that $B$ is left (right) strongly modular if and only if any element of $B$ which has zero kernel in $_RM(M_R^ * )$ has essential image in $_RM(M_R^ * )$, and that $B$ is a left (right) Utumi ring if and only if every submodule $_RU{\text {o}}{{\text {f}}_R}M(U_R^ * {\text {of }}M_R^ * )$ such that ${U^ \bot } = 0{(^ \bot }{U^ * } = 0)$ is essential in $_RM(M_R^ * )$.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 553-559
- MSC: Primary 16A08; Secondary 16A65
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826480-8
- MathSciNet review: 826480