An Approach for Δ22 - Supplemented Modules with Ideals

Abstract

The aim of this paper is to present supplemented modules and investigate their main algebraic properties. Let be an ideal of a ring and be an module. We call a module is supplemented, provided for each submodule of , there exists a direct summand of such that , and . We prove that the factor module by any fully invariant submodule remains so, when the module is supplemented. We show that any direct sum of supplemented modules preserves its supplemented property when this direct sum is a duo module. Additionally, we make comparisons of supplemented modules with other module types.