Amply Supplemented Module over Commutative Ring

Abstract

No doubt, a notion of the amply supplemented module can constitute a very important situation in the module theory, because a generalization of supplemented module depend on some types of modules as amply supplemented module. Here we introduce a characterization of the relations between amply supplemented and some concepts as, semi-perfect, perfect rings, Rad -supplemented and lifting modules. We prove that if M be a nonzero R -module is linearly compact then M is amply supplemented. Also we prove that if R be a semi-local ring with every simple R -module has a flat cover then M is amply supplemented. Let R be a Bass ring and let M be Rad -supplemented R -module then M is amply supplemented. Any lifting R -module M is amply supplemented module