2020/05/26 by Eda Yıldız, Yıldız, Eda, Ünsal Teki̇̀r +3
Mathematics · #13A15 #13C05 #54C35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2005.12983
openalex publication_date 2020/05/26 · openalex created_date 2020/06/05 · openalex updated_date 2026/07/28
In this paper, we introduce ϕ-1-absorbing prime ideals in commutative rings. Let R be a commutative ring with a nonzero identity 1≠0 and ϕ:I(R)\rightarrowI(R)∪\∅\ be a function where I(R) is the set of all ideals of R. A proper ideal I of R is called a ϕ-1-absorbing prime ideal if for each nonunits x,y,z∈ R with xyz∈ I-ϕ(I), then either xy∈ I or z∈ I. In addition to give many properties and characterizations of ϕ-1-absorbing prime ideals, we also determine rings in which every proper ideal is ϕ-1-absorbing prime.