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<p>Let <italic>R</italic> be a commutative ring with identity, and let <italic>S</italic> be a multiplicative subset of <italic>R</italic>. Then R is called a nonnil-<italic>S</italic>-Noetherian ring if every nonnil ideal of <italic>R</italic> is <italic>S</italic>-finite. Also, <italic>R</italic> is called a u-<italic>S</italic>-Noetherian ring if there exists an element <italic>s</italic> ∈ <italic>S</italic> such that for each ideal <italic>I</italic> of <italic>R</italic>, <italic>sI</italic> ⊆ <italic>K</italic> for some finitely generated sub-ideal <italic>K</italic> of <italic>I</italic>. In this paper, we examine some new characterization of nonnil-<italic>S</italic>-Noetherian rings. Then, as a generalization of nonnil-<italic>S</italic>-Noetherian rings and u-<italic>S</italic>-Noetherian rings, we introduce and investigate the nonnilu-<italic>S</italic>-Noetherian rings class.</p>
</abstract>

Let R be a commutative ring with identity, and let S be a multiplicative subset of R. Then R is called a nonnil-S-Noetherian ring if every nonnil ideal of R is S-finite. Also, R is called a u-S-Noetherian ring if there exists an element s ∈ S such that for each ideal I of R, sI ⊆ K for some finitely generated sub-ideal K of I. In this paper, we examine some new characterization of nonnil-S-Noetherian rings. Then, as a generalization of nonnil-S-Noetherian rings and u-S-Noetherian rings, we introduce and investigate the nonnilu-S-Noetherian rings class.

On nonnil-<italic>S</italic>-Noetherian and nonnil-u-<italic>S</italic>-Noetherian rings

Laboratory of Modelling and Mathematical Structures

Department of Mathematics, Faculty of Science and Technology of Fez

El Houssaine OUBOUHOU, Laboratory of Modelling and Mathematical Structures, Department of Mathematics, Faculty of Science and Technology of Fez

Department of Basic Sciences, Faculty of Engineering

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On nonnil--Noetherian and nonnil-u--Noetherian rings

Let R be a commutative ring with identity, and let S be a multiplicative subset of R. Then R is called a nonnil-S-Noetherian ring if every nonnil ideal of R is...

On nonnil-S-Noetherian and nonnil-u-S-Noetherian rings

Publié en ligne: 27 mai 2024

Pages: 201 - 220

Reçu: 27 févr. 2023

Accepté: 31 mai 2023

DOI: https://doi.org/10.2478/auom-2024-0011

Mots clés
Nonnil--Noetherian rings, Nonnil-u--Noetherian rings, Nonnil-Noetherian rings

© 2024 Najib Mahdou, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On nonnil-S-Noetherian and nonnil-u-S-Noetherian rings

Publié en ligne: 27 mai 2024

Pages: 201 - 220

Reçu: 27 févr. 2023

Accepté: 31 mai 2023

DOI: https://doi.org/10.2478/auom-2024-0011

Mots clésNonnil--Noetherian rings, Nonnil-u--Noetherian rings, Nonnil-Noetherian rings

© 2024 Najib Mahdou, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Nonnil--Noetherian rings, Nonnil-u--Noetherian rings, Nonnil-Noetherian rings