FULLY INVARIANT τM-LIFTING MODULES

Abstract

Let τM be any preradical for σM and N any module in σM. A module N is called τM-lifting if for every submodule K of N, there is a decomposition K=A⊕B, such that A is a direct summand of N and B⊆τMN. We call N is (strongly) FI‐τM-lifting if for every fully invariant submodule K of N, there is a decomposition K=A⊕B, such that A is a (fully invariant) direct summand of N and B⊆τMN. The class of FI‐τM-lifting modules properly contains the class of τM-lifting modules and the class of strongly FI‐τM-lifting modules. In this paper we investigate whether the class of (strongly) FI‐τM-lifting modules are closed under particular class of submodules, direct summands and direct sums.