On n-1-absorbing prime ideals - TEKİR, ÜNSAL (My University, 2022)
In this paper, we introduce and study n -1-absorbing prime ideals of commutative rings. Let R be a ring and n a positive integer. A proper ideal I of R is said to be an n -1-absorbing prime ideal if whenever x1x2…xn+1∈I for some nonunits x1,x2,…,xn+1∈R, then either x1x2…xn∈I or xn+1∈I. It is obvious that 1-1-absorbing (2-1-absorbing) prime ideals are exactly prime (1-absorbing prime) ideals. Various examples and characterizations of n -1-absorbing prime ideals are given.
Keywords: Matematik; Değişmeli Halkalar ve Cebirler; Temel Bilimler; Mathematics; Commutative Rings and Algebras; Natural Sciences; Temel Bilimler (SCI); Doğa Bilimleri Genel; ÇOK DİSİPLİNLİ BİLİMLER; MATEMATİK; Natural Sciences (SCI); NATURAL SCIENCES, GENERAL; MATHEMATICS; MULTIDISCIPLINARY SCIENCES; Multidisipliner; Ayrık Matematik ve Kombinatorik; Geometri ve Topoloji; Mantık; Fizik Bilimleri; Multidisciplinary; Discrete Mathematics and Combinatorics; Geometry and Topology; Logic; Physical Sciences; Prime ideal1; absorbing prime idealn; 1-absorbing prime ideal