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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 rings generated by faithful cyclic modules


Author: Gary F. Birkenmeier
Journal: Proc. Amer. Math. Soc. 100 (1987), 8-10
MSC: Primary 16A08; Secondary 16A36
MathSciNet review: 883391
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Abstract: A ring $ R$ is said to be generated by faithful cyclics (right finitely pseudo-Frobenius), denoted by right GFC (FPF), if every faithful cyclic (finitely generated) right $ R$-module generates the category of right $ R$-modules. A fundamental result in FPF ring theory, due to S. Page, is that if $ R$ is a right nonsingular right FPF ring, then $ {Q_r}(R)$ is FPF. In this paper we generalize this result by providing a necessary and sufficient condition for a right nonsingular right GFC ring to have an FPF maximal right quotient ring.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0883391-0
PII: S 0002-9939(1987)0883391-0
Keywords: Maximal right quotient ring, FPF, GFC, selfinjective, nonsingular, faithful, generator
Article copyright: © Copyright 1987 American Mathematical Society