Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2403.19659 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911818713137152 |
|---|---|
| author | Uçar, Zeynep Yılmaz Ersoy, Bayram Ali Tekir, Ünsal Koç, Suat Onar, Serkan |
| author_facet | Uçar, Zeynep Yılmaz Ersoy, Bayram Ali Tekir, Ünsal Koç, Suat Onar, Serkan |
| contents | In this paper, we study weakly classical 1-absorbing prime submodules of a nonzero unital module $M$ over a commutative ring $R$ having a nonzero identity. A proper submodule $N$ of $M$ is said to be a weakly classical 1-absorbing prime submodule, if for each $m\in M$ and nonunits $a,b,c\in R,$ $0\neq abcm\in N$ implies that $abm\in N$ or $cm\in N$. We give various examples and properties of weakly classical 1-absorbing prime submodules. Also, we investiage the weakly classical 1-absorbing prime submodules of tensor product $F\otimes M$ of a (faithfully) flat $R$-module $F$ and any $R$-module $M.$ Also, we prove that if every proper submodule of an $R$-module $M$ is weakly classical 1-absorbing prime, then $Jac(R)^{3}M=0$. In terms of this result, we characterize modules over local rings in which every proper submodule is weakly classical 1-absorbing prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19659 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On weakly classical 1-absorbing prime submodules Uçar, Zeynep Yılmaz Ersoy, Bayram Ali Tekir, Ünsal Koç, Suat Onar, Serkan Rings and Algebras 13A15, 13C05, 13C13 In this paper, we study weakly classical 1-absorbing prime submodules of a nonzero unital module $M$ over a commutative ring $R$ having a nonzero identity. A proper submodule $N$ of $M$ is said to be a weakly classical 1-absorbing prime submodule, if for each $m\in M$ and nonunits $a,b,c\in R,$ $0\neq abcm\in N$ implies that $abm\in N$ or $cm\in N$. We give various examples and properties of weakly classical 1-absorbing prime submodules. Also, we investiage the weakly classical 1-absorbing prime submodules of tensor product $F\otimes M$ of a (faithfully) flat $R$-module $F$ and any $R$-module $M.$ Also, we prove that if every proper submodule of an $R$-module $M$ is weakly classical 1-absorbing prime, then $Jac(R)^{3}M=0$. In terms of this result, we characterize modules over local rings in which every proper submodule is weakly classical 1-absorbing prime. |
| title | On weakly classical 1-absorbing prime submodules |
| topic | Rings and Algebras 13A15, 13C05, 13C13 |
| url | https://arxiv.org/abs/2403.19659 |