Weak Pseudo – 2 – Absorbing Submodules And Related Concepts

Abstract

Let R be a commutative ring with identity and E be a unitary left R – module .We introduce and study the concept Weak Pseudo – 2 – Absorbing submodules as generalization of weakle – 2 – Absorbing submodules , where a proper submodule A of an R – module E is called Weak Pseudo – 2 – Absorbing if 0 ≠rsx A for r, s R , x E , implies that rx A + soc ( E ) or sx A + soc (E) or rs [ A + soc ( E ) E ]. Many basic properties, characterizations and examples of Weak Pseudo – 2 – Absorbing submodule in some types of modules are introduced .

Keywords

• weakly – 2 – absorbing submodules , essential submodule , socal of modules , multiplication modules , z – regular modules , wp – 2 – absorbing submodules .