1. bookVolume 29 (2021): Edizione 2 (June 2021)
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Rivista
eISSN
1844-0835
Prima pubblicazione
17 May 2013
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1 volta all'anno
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Inglese
access type Accesso libero

On weakly S-prime ideals of commutative rings

Pubblicato online: 08 Jul 2021
Volume & Edizione: Volume 29 (2021) - Edizione 2 (June 2021)
Pagine: 173 - 186
Ricevuto: 11 Dec 2020
Accettato: 19 Jan 2021
Dettagli della rivista
License
Formato
Rivista
eISSN
1844-0835
Prima pubblicazione
17 May 2013
Frequenza di pubblicazione
1 volta all'anno
Lingue
Inglese
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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