Commun. Korean Math. Soc. 2024; 39(1): 71-77
Online first article January 24, 2024 Printed January 31, 2024
https://doi.org/10.4134/CKMS.c230111
Copyright © The Korean Mathematical Society.
Ali Benhissi, Abdelamir Dabbabi
Faculty of Sciences of Monastir; Faculty of Sciences of Monastir
Let $A$ be a commutative integral domain with identity element and $S$ a multiplicatively closed subset of $A$. In this paper, we introduce the concept of $S$-valuation domains as follows. The ring $A$ is said to be an $S$-valuation domain if for every two ideals $I$ and $J$ of $A$, there exists $s\in S$ such that either $sI\subseteq J$ or $sJ\subseteq I$. We investigate some basic properties of $S$-valuation domains. Many examples and counterexamples are provided.
Keywords: $S$-valuation domain, valuation domain, $S$-Noetherian
MSC numbers: Primary 13B25, 13E05, 13A15
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