Geodesic
Generalization of the $S$-Noetherian concept
Archivum mathematicum, Tome 59 (2023) no. 4, pp. 307-314 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $A$ be a commutative ring and ${\mathcal{S}}$ a multiplicative system of ideals. We say that $A$ is ${\mathcal{S}}$-Noetherian, if for each ideal $Q$ of $A$, there exist $I\in {\mathcal{S}}$ and a finitely generated ideal $F\subseteq Q$ such that $IQ\subseteq F$. In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.
Let $A$ be a commutative ring and ${\mathcal{S}}$ a multiplicative system of ideals. We say that $A$ is ${\mathcal{S}}$-Noetherian, if for each ideal $Q$ of $A$, there exist $I\in {\mathcal{S}}$ and a finitely generated ideal $F\subseteq Q$ such that $IQ\subseteq F$. In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.
DOI : 10.5817/AM2023-4-307
Classification : 13A15, 13B25, 13E05
Keywords: ${\mathcal{S}}$-Noetherian; Nagata’s idealization; multiplicative system of ideals 
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Dabbabi, Abdelamir; Benhissi, Ali. Generalization of the $S$-Noetherian concept. Archivum mathematicum, Tome 59 (2023) no. 4, pp. 307-314. doi: 10.5817/AM2023-4-307

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