1. bookVolume 29 (2021): Edizione 3 (November 2021)
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eISSN
1844-0835
Prima pubblicazione
17 May 2013
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1 volta all'anno
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access type Accesso libero

On 1-absorbing δ-primary ideals

Pubblicato online: 23 Nov 2021
Volume & Edizione: Volume 29 (2021) - Edizione 3 (November 2021)
Pagine: 135 - 150
Ricevuto: 09 Mar 2021
Accettato: 30 Apr 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 nonzero identity. Let 𝒥(R) be the set of all ideals of R and let δ : 𝒥 (R) → 𝒥 (R) be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with JI, we have Lδ (L) and δ (J) ⊆ δ (I). Let δ be an expansion function of ideals of R. In this paper, we introduce and investigate a new class of ideals that is closely related to the class of δ -primary ideals. A proper ideal I of R is said to be a 1-absorbing δ -primary ideal if whenever nonunit elements a, b, cR and abcI, then abI or cδ (I). Moreover, we give some basic properties of this class of ideals and we study the 1-absorbing δ-primary ideals of the localization of rings, the direct product of rings and the trivial ring extensions.

Keywords

MSC 2010

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