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On Almost $S$-prime submodules | ||
| Journal of Algebra and Related Topics | ||
| دوره 11، شماره 1، شهریور 2023، صفحه 27-42 اصل مقاله (343.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2022.22862.1427 | ||
| نویسندگان | ||
| F. Farzalipour* 1؛ R. Ghaseminejad2؛ M. S. Sayedsadeghi2 | ||
| 1Department of Mathematics, Payame Noor University, Tehran, Iran. | ||
| 2Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| Let $R$ be a commutative ring with non-zero identity, $S\subseteq R$ be a multiplicatively closed subset of $R$ and let $M$ be an $R$-module. A submodule $N$ of $M$ with $(N:_{R}M)\cap S=\emptyset$ is said to be almost $S$-prime, if there exists an $s\in S$ such that whenever $rm\in N-(N:_{R}M)N$, then $sm\in N$ or $sr\in (N:_{R}M)$ for each $r\in R$, $m\in M$. The aim of this paper is to introduce and investigate some properties of the notion of almost $S$-prime submodules, especially in multiplication modules. Moreover, we investigate the behaviour of this structure under module homomorphisms, localizations, quotient modules, Cartesian product. Finally, we state two kinds of submodules of the amalgamation module along an ideal and investigate conditions under which they are almost $S$-prime. | ||
| کلیدواژه‌ها | ||
| $S$-prime submodule؛ almost $S$-prime submodule؛ multiplication module | ||
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آمار تعداد مشاهده مقاله: 274 تعداد دریافت فایل اصل مقاله: 407 |
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