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Proceedings of the American Mathematical Society

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



Modules whose endomorphism rings have isomorphic maximal left and right quotient rings

Author: Soumaya Makdissi Khuri
Journal: Proc. Amer. Math. Soc. 85 (1982), 161-164
MSC: Primary 16A65
MathSciNet review: 652433
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Abstract: Let $ _RM$ be a left $ R$-module such that $ {\operatorname{Hom} _R}(M,U) \ne 0$ for any nonzero submodule $ U$ of $ M$, let $ E(M)$ denote the injective hull of $ M$, and let $ B$ (resp. $ A$) denote the ring of $ R$-endomorphisms of $ M$ (resp. $ E(M)$). It is known that if $ M$ is nonsingular then $ B$ is left nonsingular and $ A$ is the maximal left quotient ring of $ B$. We give here necessary and sufficient conditions on $ M$ for $ B$ to be right nonsingular and for $ A$ to be the maximal right quotient ring of $ B$.

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Keywords: Endomorphism rings, nonsingular modules and rings, maximal quotient rings, Utumi rings
Article copyright: © Copyright 1982 American Mathematical Society

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