Turkish Journal of Mathematics
Abstract
Let $M$ be a module over a commutative ring $R.$ A proper submodule $N$ of $M$ is called weakly $2$-absorbing, if for $r,s\in R$ and $x\in M$ with $0\neq rsx\in N,$ either $rs\in (N:M)$ or $rx\in N$ or $sx\in N.$ We study the behavior of $(N:M)$ and $\sqrt{(N:M)},$ when $N$ is weakly $2$-absorbing. The weakly $2$-absorbing submodules when $R=R_1\oplus R_2$ are characterized. Moreover we characterize the faithful modules whose proper submodules are all weakly $2$-absorbing.
DOI
10.3906/mat-1501-55
Keywords
Prime submodule, $2$-absorbing submodule, weakly $2$-absorbing submodule, weakly prime submodule, weak prime submodule
First Page
350
Last Page
364
Recommended Citation
MORADI, S, & AZIZI, A (2016). Weakly $2$-absorbing submodules of modules. Turkish Journal of Mathematics 40 (2): 350-364. https://doi.org/10.3906/mat-1501-55
