Rings with Ascending Condition on Annihilators

1 February 1966

journal article
research article
Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal

Vol. 27 (1) , 179-191
https://doi.org/10.1017/s0027763000011983

Abstract

Quasi-frobenius (= QF) rings have many interesting characterizations. One such, due to Ikeda [17] is that these rings are right (left) artinian and right (left) self-injective. Thus, if R is QF, then R is right (left) noetherian, so each direct sum of injective right R-modules is injective: in particular, each free, hence, each projective, R-module is injective. One object of this paper is to report that this property characterizes QF-rings:

Keywords

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