Notes on FI-Soc -lifting modules

Notes on FI-Soc -lifting modules

Let M be any module. A module M is called FI-Soc-lifting if for every fully invariant submodule K of M, there is a decomposition K = A CD B, such that A is a direct Summand of M and B C Soc (M). In this paper we investigate whether the class of FI-Soc-lifting modules are closed under particular class of direct sums.