ON LIFTING BAER MODULES

We introduce the notion of lifting Baer modules, as a generalization of both Baer and lifting modules and give some of their properties. A module M is called lifting Baer if right annihilator of a left ideal of End(M) lies above a direct summand of M. Also, we define the concepts of r-supplemented and amply r-supplemented modules. It is shown that an amply r-supplemened module M that every supplement submodule, is a direct summand of M, is lifting Baer. The relationships between Baer modules and lifting Baer modules are investigated. Morever, we prove that the endomorphism ring of any lifting Baer module is lifting Baer ring.