Large-Coessential and Large-Coclosed Submodules

Abstract

The goal of this research is to introduce the concepts of Large-coessential submodule and Large-coclosed submodule, for which some properties are also considered. Let M be an R-module and K, N are submodules of M such that , then K is said to be Large-coessential submodule, if . A submodule N of M is called Large-coclosed submodule, if K is Large-coessential submodule of N in M, for some submodule K of N, implies that .

e*-Extending Modules

“…In this section, we will introduce a new concept which is a generalization of coclosed, and prove some properties as in [10] and [11]. Definition 3.1 [7] Let 𝑇 ≤ 𝑆 be submodules of 𝑀 .When 2.…”