Czechoslovak Mathematical Journal, first online, pp. 1-23
On $S$-1-absorbing primary submodules
Mohammed ISSOUAL, Najib MAHDOU, Ece YETKİN ÇELİKEL, Neslihan Ayşen ÖZBAY
Received January 26, 2026. Published online August 27, 2026.
Abstract: We introduce the notion of $S$-1-absorbing primary submodule as an extension of 1-absorbing primary submodules. Let $S$ be a multiplicatively closed subset of a ring $R$ and $M $ be an $R $-module. A submodule $N$ of $M$ with $(N:_RM)\cap S=\emptyset$ is said to be $S$-1-absorbing primary if there exists $s \in S$ such that whenever $abm\in N$ for some non-units $a,b\in R$ and $m\in M$, then either $sab\in(N:_RM)$ or $sm\in M$-$rad(N)$. We examine several properties of this concept and provide some characterizations. In addition, $S$-1-absorbing primary avoidance theorem and $S$-1-absorbing primary property for idealization and amalgamation are presented.
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Affiliations: Mohammed Issoual, CRMEF Khmisset, Khmisset, Morocco, e-mail: issoual2@yahoo.fr; Najib Mahdou, Laboratory of Modeling and Mathematical Structures, Department of Mathematics, Faculty of Science and Technology, University S.M. Ben Abdellah, Fez, Box 2202, Morocco, e-mail: mahdou@hotmail.com; Ece Yetkin Çelikel, Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University, Gaziantep, Turkey, e-mail: ece.celikel@hku.edu.tr, yetkinece@gmail.com; Neslihan Ayşen Özbay (corresponding author), Department of Mathematics, Faculty of Arts and Sciences, Çankaya University, Mimar Sinan Street No: 4, Ankara, 06815, Turkey, e-mail: ozbay@cankaya.edu.tr
