Weak pseudo quasi-2-absorbing submodules and related concepts

Abstract EN

In this paper R stand for commutative ring with identity ,and E is a unitary left R-module.

The concept of weakly quasi-2-Absorbing submodule has been generalized in this research to a Wpq-2-Absorbing submodules ,where a paper submodule H of an R-module E is a Wpq-2-Absorbiming if 0≠abcyϵH ,for a,b,cϵR, yϵE , implies that either abyϵH+Soc(E) or acyϵH+Soc(E) or bcyϵH+Soc(E) .Several characterizations ,examples and basic properties of this concept are introduced .Moreover characterizations of Wpq-2-Absorbing submodules in some types of modules are given .Keywords: Weakly quasi-2-Absorbing submodules, Wpq-2-Absorbing submodules, socel of modules ,multiplication modules ,Z-regular modules ,non-singular modules.