On µ-lifting modules

Abstract EN

Let R be a ring with identity and let M be a left R-module.

M is called µ-lifting modulei f for every sub module A of M, There exists a direct summand D of M such that M = D D', for some sub module D' of M such that A≤D and A D'<<µ D'.The aim of this paper is to introduce properties of µ-lifting modules.

Especially, we give characterizations of µ-lifting modules.

On the other hand, the notion of amply µ-supplemented iis studied as a generalization of amply supplemented modules, we show that if M is amply µ-supplemented such that every µ-supplement sub module of M is a direct summand, then M is µ-lifting module.

Finally, we give some conditions under which the quotient and direct sum of µ-lifting modules is µ-lifting.