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Generalization of the S -Noetherian concept

Abdelamir DabbabiAli Benhissi — 2023

Archivum Mathematicum

Let A be a commutative ring and 𝒮 a multiplicative system of ideals. We say that A is 𝒮 -Noetherian, if for each ideal Q of A , there exist I 𝒮 and a finitely generated ideal F Q such that I Q F . In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.

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