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 and delimit our results.