Motivated by , 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.
"On \tau-lifting Modules and \tau-semiperfect Modules,"
Turkish Journal of Mathematics: Vol. 33:
2, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol33/iss2/3