Amalgamated algebras along an ideal defined by 1-absorbing-like conditions

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El Khalfi A., Kolotoğlu T., Mahdou N., Tekir Ü., Ersoy B. A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.22, no.1, pp.1-10, 2023 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 22 Issue: 1
• Publication Date: 2023
• Doi Number: 10.1142/s0219498824500907
• Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
• Page Numbers: pp.1-10
• Yıldız Technical University Affiliated: Yes

Abstract

Let R" role="presentation" >R$�$ be a commutative ring with nonzero identity. A proper ideal I" role="presentation" >I$�$ of R" role="presentation" >R$�$ is called a 1-absorbing prime ideal (respectively, 1-absorbing primary ideal) if whenever nonunit elements a,b,c∈R" role="presentation" >a,b,c∈R$�,�,�\in �$ with abc∈I," role="presentation" >abc∈I,$���\in �,$ then ab∈I" role="presentation" >ab∈I$��\in �$ or c∈I" role="presentation" >c∈I$�\in �$ (respectively, ab∈I" role="presentation" >ab∈I$��\in �$ or c∈I" role="presentation" >c∈I–√$�\in \sqrt{�}$). The purpose of this paper is to study the transfer of certain 1-absorbing-like properties to amalgamation of A" role="presentation" >A$�$ with B" role="presentation" >B$�$ along J" role="presentation" >J$�$ with respect to f" role="presentation" >f$�$ (denoted by A⋈fJ" role="presentation" >A⋈fJ$�{\bowtie }^{�}�$), introduced and studied by D’Anna, Finocchiaro and Fontana. Our results provide new techniques for the construction of new original examples satisfying the above-mentioned properties.