Akademik Veri Yönetim Sistemi
Turkish Journal of Mathematics, cilt.33, sa.2, ss.117-130, 2009 (SCI-Expanded)
Motivated by [1], we study on τ-lifting modules (rings) and τ-semiperfect modules (rings) for a preradical τ and give some equivalent conditions. We prove that; i)if M is a projective τ-lifting module with τ(M) ⊆ δ(M), then M has the finite exchange property; ii)if R is a left hereditary ring and τ is a left exact preradical, then every τ-semiperfect module is τ-lifting; iii) R is τ-lifting if and only if every finitely generated free module is τ-lifting if and only if every finitely generated projective module is τ-lifting; iv) if τ(R) ⊆ δ(R), then R is τ-semiperfect if and only if every finitely generated module is τ-semiperfect if and only if every simple R-module is τ-semiperfect. © TÜBI{dotless}TAK.