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On Semiperfect FPF-Rings

Published online by Cambridge University Press:  20 November 2018

Mohamed Yousif*
Affiliation:
Department of Mathematics, The Ohio State University, Lima Campus Lima, Ohio 45804 U.S.A.
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Abstract

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We show that a semiperfect right FPF-ring is right self-injective if and only if J(R) — Z(RR), extending a well-known result due to Carl Faith on semiperfect right FPF-rings with nil Jacobson radical.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Camillo, Victor, How injective is a semiperfect FPF ring?, Comm. Algebra 17(1989), 19511954.Google Scholar
2. Faith, Carl, Injective Cogenerator rings and a theorem of Tachikawa, Proc. Amer. Math. Soc. 60(1976), 2530.Google Scholar
3. Faith, Carl and Page, Stanley, FPF Ring Theory, London Math. Soc. Lect. Notes 88, Cambridge Univ. Press, 1984.Google Scholar
4. Faticoni, Theodore G., FPF rings I: The Noetherian Case, Comm. Algebra 13(1985), 21192136.Google Scholar
5. Osofsky, Barbara, A Generalization of quasi-Frobenius rings, J. Algebra 4(1966), 373387.Google Scholar
6. Tachikawa, Hiroyuki, A Generalization of quasi-F rob enius rings, Proc. Amer. Math. Soc. 20(1969), 471 476.Google Scholar