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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
Article . 2021 . Peer-reviewed
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On weakly S -prime ideals of commutative rings

Authors: Almahdi Fuad Ali Ahmed; Bouba El Mehdi; Tamekkante Mohammed;

On weakly S -prime ideals of commutative rings

Abstract

Abstract Let R be a commutative ring with identity and S be a multiplicative subset of R . In this paper, we introduce the concept of weakly S -prime ideals which is a generalization of weakly prime ideals. Let P be an ideal of R disjoint with S . We say that P is a weakly S -prime ideal of R if there exists an s ∈ S such that, for all a, b ∈ R , if 0 ≠ ab ∈ P , then sa ∈ P or sb ∈ P . We show that weakly S -prime ideals have many analog properties to these of weakly prime ideals. We also use this new class of ideals to characterize S -Noetherian rings and S -principal ideal rings.

Keywords

secondary 13b02, 13e99, primary 13a15, QA1-939, nagata idealization, weakly s-prime ideals, s-noetherian rings, s-prime ideals, Mathematics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Top 10%
Average
Top 10%
Published in a Diamond OA journal
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