Weakly Quasi 2-Absorbing submodule

Abstract

“Let R be a commutative ring with identity , and M is a unitary left R-module”, “A proper submodule E of an R-module M is called a weakly quasi-prime if whenever r, s ∈ R, m ∈ M, with 0 ≠ rsm ∈ E , implies that rm ∈ E or sm ∈ E”. “We introduce the concept of a weakly quasi 2-absorbing submodule as a generalization of weakly quasi-prime submodule”, where a proper submodule E of M is called a weakly quasi 2-absorbing submodule if whenever r,s,t ∈ R, m ∈M with  0≠ rstm ∈ E , implies that rsm ∈ E or rtm ∈ E or stm ∈ E. we study the basic properties of weakly quasi 2-absorbing. Furthermore, the relationships of weakly quasi 2-absorbing submodule with other classes of module are elistraited.

http://dx.doi.org/10.25130/tjps.23.2018.118