Strongly nearly-2-absorbing submodules

Abstract

Let Ɍ be a commutative ring with identity and V be a unitary left Ɍ-module. The concept of Strongly Nearly-2-Absorabing sub-modules as a generalization of Endo-2-Absorabing sub-modules and strong form of Nearly-2-Absorabing sub-modules are introduced in this paper. Many examples, basic properties of this concept are introduced. Furthermore we prove that in class of (scalar, cyclic and finitely-generated) modules the two concepts Nearly-2-Absorabing sub-modules and Strongly Nearly-2-Absorabing sub-modules are equivalent. Moreover we prove that Endo-2-Absorabing and Strongly Nearly-2-Absorabing sub-modules are equivalent in class of (semi simple, regular) modules. Also those concepts are equivalent in class of all modules over a v-ring. Finally we prove several characterizations of Strongly Nearly-2-Absorabing sub-modules in some types of modules such as (projective, faithful and content) modules in class of cyclic modules.