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Turkish Journal of Mathematics

Authors

MUSTAFA ALKAN

DOI

10.3906/mat-0801-28

Abstract

Motivated by [1], we study on \tau-lifting modules (rings) and \tau-semiperfect modules (rings) for a preradical \tau and give some equivalent conditions. We prove that; i) if M is a projective \tau-lifting module with \tau(M) \subseteq \delta(M), then M has the finite exchange property; ii) if R is a left hereditary ring and \tau is a left exact preradical, then every \tau-semiperfect module is \tau--lifting; iii) R is \tau-lifting if and only if every finitely generated free module is \tau-lifting if and only if every finitely generated projective module is \tau-lifting; iv) if \tau (R) \subseteq \delta (R), then R is \tau-semiperfect if and only if every finitely generated module is \tau-semiperfect if and only if every simple R--module is \tau-semiperfect.

First Page

117

Last Page

130

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Mathematics Commons

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