ON WEAKLY 2-ABSORBING PRIMARY SUBMODULES OF MODULES OVER COMMUTATIVE RINGS

Abstract

Assume that M is an R-module where R is a commutative ring. A proper submodule N of M is called a weakly 2-absorbing primary submodule of M if 0 not equal abm is an element of N for any a, b is an element of R and m is an element of M, then ab is an element of (N : M) or am is an element of M-rad(N) or bm is an element of M-rad(N). In this paper, we extended the concept of weakly 2-absorbing primary ideals of commutative rings to weakly 2-absorbing primary submodules of modules. Among many results, we show that if N is a weakly 2-absorbing primary submodule of M and it satisfies certain condition 0 not equal I1I2K subset of N for some ideals I-1,I-2 of R and submodule K of M, then I1I2 subset of (N : M) or I1K subset of M-rad(N) or I2K subset of M-rad(N).