1. bookVolume 29 (2021): Edition 2 (June 2021)
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eISSN
1844-0835
Première parution
17 May 2013
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access type Accès libre

On weakly S-prime ideals of commutative rings

Publié en ligne: 08 Jul 2021
Volume & Edition: Volume 29 (2021) - Edition 2 (June 2021)
Pages: 173 - 186
Reçu: 11 Dec 2020
Accepté: 19 Jan 2021
Détails du magazine
License
Format
Magazine
eISSN
1844-0835
Première parution
17 May 2013
Périodicité
1 fois par an
Langues
Anglais
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 sS such that, for all a, bR, if 0 ≠ abP, then saP or sbP. 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

MSC 2010

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