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


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" > be a commutative ring with nonzero identity. A proper ideal I" role="presentation" > of R" role="presentation" > is called a 1-absorbing prime ideal (respectively, 1-absorbing primary ideal) if whenever nonunit elements a,b,c∈R" role="presentation" >,, with abc∈I," role="presentation" >, then ab∈I" role="presentation" > or c∈I" role="presentation" > (respectively, ab∈I" role="presentation" > or c∈I" role="presentation" >). The purpose of this paper is to study the transfer of certain 1-absorbing-like properties to amalgamation of A" role="presentation" > with B" role="presentation" > along J" role="presentation" > with respect to f" role="presentation" > (denoted by A⋈fJ" role="presentation" >), 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.