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 {\rm 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.‎

Keywords:

lifting Baer module , Baer module , lifting module , Annihilators , Endomorphism rings