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

 

On quotient rings of trivial extensions


Author: Yoshimi Kitamura
Journal: Proc. Amer. Math. Soc. 88 (1983), 391-396
MSC: Primary 16A08; Secondary 16A65
MathSciNet review: 699400
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Abstract: Let $ R$ be a ring with identity and $ M$ a two-sided $ R$-module. It is shown that every right quotient ring in the sense of Gabriel of the trivial extension of $ R$ by $ M$ is a trivial extension of a right quotient ring of $ R$ by a suitable two-sided module in case $ _RM$ is flat and finitely generated by elements which centralize with every element of $ R$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699400-4
PII: S 0002-9939(1983)0699400-4
Keywords: Trivial extension, quotient ring, injective module, biendomorphism ring
Article copyright: © Copyright 1983 American Mathematical Society