Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1982-0652433-5
MathSciNet review: 652433
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A65

Retrieve articles in all journals with MSC: 16A65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0652433-5
Keywords: Endomorphism rings, nonsingular modules and rings, maximal quotient rings, Utumi rings
Article copyright: © Copyright 1982 American Mathematical Society