On n -1-absorbing prime ideals
Journal of Algebra and its Applications, cilt.22, sa.10, 2023 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 22 Sayı: 10
- Basım Tarihi: 2023
- Doi Numarası: 10.1142/s0219498823502079
- Dergi Adı: Journal of Algebra and its Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
- Anahtar Kelimeler: 1-absorbing prime ideal, n -1-absorbing prime ideal, Prime ideal
- Marmara Üniversitesi Adresli: Evet
Özet
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.