On a Generalization of Lifting Modules via SSP-Modules

In this work, we are interested in introducing a new generalization of lifting modules, namely SSP-lifting modules. This definition generalizes two concepts lifting modules and SSP-modules (modules with sum of each two summands is a summand). We show that every direct summand of a SSP-lifting module inherits the property, while a direct summand of a SIP- extending module is not SIP-extending, in general. We provide a condition which under a direct sum of SSP-lifting modules is SSP-lifting. If R =Matm(S), then we prove R is a right SSP-lifting ring if and only if the free right S-module S^m is a SSP-lifting module.