Weak pseudo–2–absorbing submodules and related concepts

Abstract EN

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 – orbing submodules as generalization of weakle – 2 – orbing submodules, where a proper submodule A of an R – module E is called Weak Pseudo – 2 – orbing 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 ): _(R )E ].

Many basic properties, characterizations and examples of Weak Pseudo – 2 – orbing submodule in some types of modules are introduced.