Modules whose endomorphism rings have isomorphic maximal left and right quotient rings
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- by Soumaya Makdissi Khuri PDF
- Proc. Amer. Math. Soc. 85 (1982), 161-164 Request permission
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 $B$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 161-164
- MSC: Primary 16A65
- DOI: https://doi.org/10.1090/S0002-9939-1982-0652433-5
- MathSciNet review: 652433