1. bookVolume 29 (2021): Edition 3 (November 2021)
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eISSN
1844-0835
Première parution
17 May 2013
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access type Accès libre

On 1-absorbing δ-primary ideals

Publié en ligne: 23 Nov 2021
Volume & Edition: Volume 29 (2021) - Edition 3 (November 2021)
Pages: 135 - 150
Reçu: 09 Mar 2021
Accepté: 30 Apr 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 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 J ⊆ I, we have L ⊆ δ (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, c ∈ R and abc ∈ I, then ab ∈ I or c ∈ δ (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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