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Rings with Ascending Condition on Annihilators

Published online by Cambridge University Press:  22 January 2016

Carl Faith
Carl Faith*
Affiliation:
Institute for Defense Analyses Princeton, New Jersey
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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:

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 1 , February 1966 , pp. 179 - 191
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

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