University of Guilan Journal of Algebra and Related Topics 2345-3931 11 1 2023 06 01 On Almost ‎$‎S‎$‎-prime submodules 27 42 6769 10.22124/jart.2022.22862.1427 EN F. Farzalipour Department of Mathematics, Payame Noor University, Tehran, Iran. R. Ghaseminejad Department of Mathematics, Payame Noor University, Tehran, Iran M. S. Sayedsadeghi Department of Mathematics, Payame Noor University, Tehran, Iran Journal Article 2022 08 30 ‎‎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. https://jart.guilan.ac.ir/article_6769_3e4565fcd00a15dd5e41046a6ed28b8c.pdf