Copy For Citation
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 with abc∈I," role="presentation" >abc∈I, then ab∈I" role="presentation" >ab∈I or c∈I" role="presentation" >c∈I (respectively, ab∈I" role="presentation" >ab∈I or c∈I" role="presentation" >c∈I–√). 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), 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.