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Some results on ϕ-primary submodules | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 12، دوره 16، شماره 10، دی 2025، صفحه 125-129 اصل مقاله (369.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.33810.5051 | ||
| نویسندگان | ||
| Mohammad Hosein Moslemi Koopaei1؛ Masoud Zolfaghari* 2 | ||
| 1Department of Mathematics, Roudehen Branch, Islamic Azad University, Roudehen, Iran | ||
| 2Department of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran | ||
| تاریخ دریافت: 03 اردیبهشت 1403، تاریخ پذیرش: 06 خرداد 1403 | ||
| چکیده | ||
| Let $R$ be a commutative ring with identity, $M$ be an unitary $R$-module, let $\mathcal{S}(M)$ be the set of all submodules of $M$ and $\phi : \mathcal{S}(M)\rightarrow \mathcal{S}(M)\cup \lbrace\emptyset\rbrace$ be a function. A proper submodule $N$ of $M$ is called $\phi$-pimary submodule if $rx\in N \setminus \phi(N)$ where $r\in R$ and $x\in M$, implies that $x\in N$ or $r\in \sqrt{(N:M)}$. In this work, $\phi$-primary submodules are studied, and some results are obtained. | ||
| کلیدواژهها | ||
| ϕ-prime ideal؛ ϕ-primary ideal؛ ϕ-prime submodule؛ ϕ-primary submodule | ||
| مراجع | ||
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