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On Self-Injective Perfect Rings

Published online by Cambridge University Press:  20 November 2018

Dolors Herbera  and
Ahmad Shamsuddin
Dolors Herbera
Affiliation:
Department of Mathematics, American University of Beirut, Beirut, Lebanon
Ahmad Shamsuddin
Affiliation:
Department de Matemàtiques, Universitat Autonoma de Barcelona, 08193 Bellatera (Barcelona), Spain
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Abstract

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Let R be a left and right perfect right self-injective ring. It is shown that if the radical of R is countably generated as a left ideal then R is quasi-Frobenius. It is also shown that the same conclusion can be drawn if r(A ∩ B) = r(A) + r(B) for all left ideals A and B of R.

Keywords

16D5016L30Perfect ringsSelf-injective ringsQuasi-Frobenius ringsInjective EnvelopeSemi-local rings
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996 , pp. 55 - 58
Copyright
Copyright © Canadian Mathematical Society 1995

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