PS-lifting modules - Kaynar, Engin (Ukrains’kyi Matematychnyi Zhurnal, 2026)
UDC 512.55 Let R be a ring and let M be a left R-module. We say that M is ps-lifting if every submodule N of M contains a direct summand X of M such that NX is projective semisimple. We present some properties of these modules. It is shown that: (1) if a projective module is ps-lifting, then it is hereditary; (2) for a ring R, every left R-module is ps-lifting if and only if every R-module is a direct sum of an injective module and a projective semisimple module; (3) _RR is ps-lifting if and only if RSoc(R) is semisimple and R is hereditary.