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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quotient rings of endomorphism rings of modules with zero singular submodule


Authors: John Hutchinson and Julius Zelmanowitz
Journal: Proc. Amer. Math. Soc. 35 (1972), 16-20
MSC: Primary 16A40
MathSciNet review: 0297805
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Abstract: Throughout this paper (R, M, N, S) will denote a Morita context satisfying a certain nonsingularity condition. For such contexts we give necessary and sufficient conditions in terms of M and R for S to have a semisimple maximal left quotient ring; respectively a full linear maximal left quotient ring, a semisimple classical left quotient ring. In doing so we extend the corresponding well-known theorems for rings (employing them in the process) to endomorphism rings.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0297805-X
PII: S 0002-9939(1972)0297805-X
Keywords: Endomorphism rings, Morita contexts, singular submodule, quotient rings, full linear rings, Goldie dimension
Article copyright: © Copyright 1972 American Mathematical Society