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

 

Semiperfect FPF rings


Author: S. S. Page
Journal: Proc. Amer. Math. Soc. 89 (1983), 395-401
MSC: Primary 16A51; Secondary 16A08, 16A36, 16A48, 16A52
MathSciNet review: 715852
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Abstract: In this paper we derive some of the structure of semiperfect FPF rings. A ring is right FPF if every f.g. faithful right module is a generator. For semiperfect right and left FPF rings we show that if all one sided zero divisors are two sided zero divisors, then the classical and maximal quotient rings coincide (all four of them) and are self-injective. We show that if the intersection of the powers of the Jacobson radical is zero, then right and left regular elements are regular. Also, we show right FPF semiperfect rings contain the singular submodule of their injective hulls and that every finitely generated module contained in the injective hull and containing the ring is isomorphic to the ring.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0715852-5
PII: S 0002-9939(1983)0715852-5
Article copyright: © Copyright 1983 American Mathematical Society