TURKISH JOURNAL OF MATHEMATICS, cilt.33, sa.2, ss.117-130, 2009 (SCI-Expanded)
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.