M-Cofaithful modules and correspondences of closed submodules with coclosed submodule

Authors : T AMOUZEGAR, Y TALEBİ

Pages : 1307-1313

View : 22 | Download : 9

Publication Date : 2015-12-01

Article Type : Research Paper

Abstract :In this paper we introduce and investigate M -cofaithful modules. A module N ∈ σ [ M ] is called M -cofaithful if for every $0\neq$   f ∈ H om R insert ignore into journalissuearticles values( N,X ); with X ∈ σ [ M ] , Hom$_R insert ignore into journalissuearticles values( X,M ); f \neq 0 $ . We show that if N is an M -cofaithful weak supplemented module and Hom R insert ignore into journalissuearticles values( N, M ); a noetherian S -module, then there exists an order-preserving correspondence between the coclosed R -submodules of N and the closed S -submodules  of Hom R insert ignore into journalissuearticles values( N,M ); , where S = End R insert ignore into journalissuearticles values( M ); . Some applications are: insert ignore into journalissuearticles values(1); the , connection between M` s being a lifting module and End R insert ignore into journalissuearticles values( M );` s being an extending ring; insert ignore into journalissuearticles values(2); the equality between the hollow dimension of a quasi-injective coretractable module M and the uniform dimension of End R insert ignore into journalissuearticles values( M ); . 
Keywords : M Cofaithful modules, Coretractable modules, Closed and coclosed submodules