Turkish Journal of Mathematics
DOI
10.3906/mat-1501-55
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.
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, SEDIGHEH and AZIZI, ABDULRASOOL
(2016)
"Weakly $2$-absorbing submodules of modules,"
Turkish Journal of Mathematics: Vol. 40:
No.
2, Article 10.
https://doi.org/10.3906/mat-1501-55
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss2/10
