Publication: Amalgamated algebras along an ideal defined by 1-absorbing-like conditions
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Date
2023-01-01
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Abstract
Let R be a commutative ring with nonzero identity. A proper ideal I of R is called a 1-absorbing prime ideal (respectively, 1-absorbing primary ideal) if whenever nonunit elements a,b,c∈R with abc∈I, then ab∈I or c∈I (respectively, ab∈I or c∈I–√). The purpose of this paper is to study the transfer of certain 1-absorbing-like properties to amalgamation of A with B along J with respect to f (denoted by A⋈fJ), 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.
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Temel Bilimler, Natural Sciences, Temel Bilimler (SCI), Doğa Bilimleri Genel, ÇOK DİSİPLİNLİ BİLİMLER, Natural Sciences (SCI), NATURAL SCIENCES, GENERAL, MULTIDISCIPLINARY SCIENCES, Multidisipliner, Multidisciplinary, absorbing prime ideal, absorbing primary ideal, amalgamated algebra along an ideal
Citation
El Khalfi A., Kolotoğlu T., Mahdou N., Tekir Ü., Ersoy B. A., "Amalgamated algebras along an ideal defined by 1-absorbing-like conditions", JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.1, ss.1-12, 2023