On H-Âµ-supplemented modules

Enas Mustafa Kamil; Wasan Khalid

doi:10.24996/ijs.2019.60.5.21

Authors

Enas Mustafa Kamil Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Wasan Khalid Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2019.60.5.21

Keywords:

Âµ relation, H-Âµ-supplemented modules

Abstract

Weosay thatotheosubmodules A, B ofoan R-module Moare Âµ-equivalent , AÂµB ifoand onlyoif <<_Âµand <<_Âµ. Weoshow thatoÂµ relationois anoequivalent relationoand hasegood behaviorywith respectyto additionmof submodules, homorphismsr, andydirectusums, weaapplyothese resultsotoointroduced theoclassoof H-Âµ-supplementedomodules. Weosay thatoa module Mmis H-Âµ-supplementedomodule ifofor everyosubmodule A of M, thereois a directosummand D ofoM suchothat AÂµD. Variousoproperties ofothese modulesoarepgiven.