On µ-Semiregular Module

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.

F-µ-Semiregular Modules

“…An R-module M is called µ-semiregular module if there exists a decomposition M=A⨁B, such that A is projective submodule of N and [5]. This concept leads us to introduce the following concept; Let M be an R-module F be a submodule of M ,and x∊M.…”

“…But Therefore, K is F-µ-semiregular. Recall that M is called µ-semi hollow module if every finitely generated proper submodule of M is µ-small submodule of M [ 5] . 3-N can be written as N = A  S, where A is a projective summand of M and S F. F. Let : R⟶ be defined by (x)= rx , ∀ r∊ R. be an epimorphism, and : ⟶A be the projection homomorphism , then, clearly, ₒ = :R⟶A is an epimorphism.…”