Pseudo primary-2-absorbing submodules and some related concepts

Abstract EN

Let R be a commutative ring with identity.

The aim of this paper is introduce the notion of a pseudo primary-2-absorbing submodule as generalization of 2-absorbing submodule and a pseudo-2-absorbing submodules.

A proper submodule K of an ft-module W is called pseudo primary-2-absorbing if whenever rsxeK, for r,sER, xeW, implies that either rx e W — rad(K) + soc(W) or sx e W — rad(K) + soc(W) or rsW £ K + soc(W).

Many basic properties, examples and characterizations of these concepts are given.

Furthermore, characterizations of pseudo primary-2-absorbing submodules in some classes of modules are introduced.

Moreover, the behavior of a pseudo primary-2-absorbing submodule under ft-homomorphism is studied.