On lifting Baer modules

Document Type : Research Paper

Authors

Department of Mathematics, University of Mazandaran, Babolsar, Iran

Abstract

‎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.‎

Keywords


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