AN APPROACH FOR δ_SS-SUPPLEMENTED MODULES WITH IDEALS

Abstract

The aim of this paper is to present J_(δ_ss-)supplemented modules and investigate their main algebraic properties. Let J be an ideal of a ring S and A be an S-module. We call a module A is J_(δ_ss )-supplemented, provided for each submodule B of A, there exists a direct summand C of A such that A=B+C, B∩C≤JC and B∩C≤〖Soc〗_δ (C). We prove that the factor module by any fully invariant submodule remains so, when the module is J_(δ_ss )-supplemented. We show that any direct sum of J_(δ_ss )-supplemented modules preserves its J_(δ_ss )-supplemented property when this direct sum is a duo module. Additionally, we make comparisons of J_(δ_ss )-supplemented modules with other module types.