On strongly PI-lifting modules

In this paper, the class of strongly pi-lifting modules is introduced and investigated. the connections between strongly pi-lifting modules and the generalizations of lifting modules are presented. we provide that the class of strongly pi-lifting modules is contained in the class of pi-lifting modules. moreover, it is proved that for an abelian ring r, r is pi-lifting as a right r-module if and only if r/i has a projective cover for every right ideal i of r. the structural properties of strongly pi-lifting modules are determined, and examples are provided to exhibit our results.