تقرير
On weakly classical 1-absorbing prime submodules
| العنوان: | On weakly classical 1-absorbing prime submodules |
|---|---|
| المؤلفون: | Uçar, Zeynep Yılmaz, Ersoy, Bayram Ali, Tekir, Ünsal, Koç, Suat, Onar, Serkan |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Rings and Algebras, 13A15, 13C05, 13C13 |
| الوصف: | 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. Comment: 16 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.19659 |
| رقم الأكسشن: | edsarx.2403.19659 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |