On µ-Semiregular Module

Abstract

Abstract Let R be an associative ring with identity and let M be right R-module M is called μ-semi hollow module if every finitely generated submodule of M is μ-small submodule of M The purpose of this paper is to give some properties of μ-semi hollow module. Also, we gives conditions under, which the direct sum of μ-semi hollow modules is μ-semi hollow. An R-module is said has a projective μ-cover if there exists an epimorphism f:P→M Where P is a projective R-module and ker (f)≪ P.And study some properties of Projective μ-cover of M. Were studied Moreover, An module M is μ-semiregular module if every cyclic submodule of M is μ-lying summand of M We add some results of μ-semiregular module.