On t-lifting Modules and t-semiperfect Modules

Authors : Mustafa ALKAN

Pages : 117-130

View : 10 | Download : 6

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Motivated by [1], we study on t-lifting modules insert ignore into journalissuearticles values(rings); and t-semiperfect modules insert ignore into journalissuearticles values(rings); for a preradical t and give some equivalent conditions. We prove that; i); if M is a projective t-lifting module with tinsert ignore into journalissuearticles values(M); \subseteq dinsert ignore into journalissuearticles values(M);, then M has the finite exchange property; ii); if R is a left hereditary ring and t is a left exact preradical, then every t-semiperfect module is t--lifting; iii); R is t-lifting if and only if every finitely generated free module is t-lifting if and only if every finitely generated projective module is t-lifting; iv); if t insert ignore into journalissuearticles values(R); \subseteq d insert ignore into journalissuearticles values(R);, then R is t-semiperfect if and only if every finitely generated module is t-semiperfect if and only if every simple R--module is t-semiperfect.
Keywords : t lifting modules, Projective t covers, t supplement submodules, t semiperfect modules