On tau-lifting Modules and tau-semiperfect Modules

ALKAN M.

TURKISH JOURNAL OF MATHEMATICS, vol.33, no.2, pp.117-130, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 2
  • Publication Date: 2009
  • Doi Number: 10.3906/mat-0801-28
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.117-130
  • Keywords: tau-lifting modules, Projective tau-covers, tau-supplement submodules, tau-semiperfect modules, PERFECT, RESPECT
  • Akdeniz University Affiliated: Yes

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) subset of 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) subset of 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.