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.
Farzalipour, F., Ghaseminejad, R., & Sayedsadeghi, M. S. (2023). On Almost $S$-prime submodules. Journal of Algebra and Related Topics, 11(1), 27-42. doi: 10.22124/jart.2022.22862.1427
MLA
F. Farzalipour; R. Ghaseminejad; M. S. Sayedsadeghi. "On Almost $S$-prime submodules". Journal of Algebra and Related Topics, 11, 1, 2023, 27-42. doi: 10.22124/jart.2022.22862.1427
HARVARD
Farzalipour, F., Ghaseminejad, R., Sayedsadeghi, M. S. (2023). 'On Almost $S$-prime submodules', Journal of Algebra and Related Topics, 11(1), pp. 27-42. doi: 10.22124/jart.2022.22862.1427
VANCOUVER
Farzalipour, F., Ghaseminejad, R., Sayedsadeghi, M. S. On Almost $S$-prime submodules. Journal of Algebra and Related Topics, 2023; 11(1): 27-42. doi: 10.22124/jart.2022.22862.1427
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