On ϕ-1-absorbing prime ideals
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, cilt.62, ss.907-918, 2021 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 62
- Basım Tarihi: 2021
- Doi Numarası: 10.1007/s13366-020-00557-w
- Dergi Adı: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Sayfa Sayıları: ss.907-918
- Anahtar Kelimeler: phi-prime ideal, 1-absorbing prime ideal, phi-1-absorbing prime ideal, Generalizations of prime ideal, 2-ABSORBING IDEALS
- Marmara Üniversitesi Adresli: Evet
Özet
In this paper, we introduce phi-1-absorbing prime ideals in commutative rings. Let R be a commutative ring with a nonzero identity 1 not equal 0 and phi : I(R) -> I(R) boolean OR {theta} be a function where I( R) is the set of all ideals of R. A proper ideal I of R is called a phi-1-absorbing prime ideal if for each nonunits x, y, z is an element of R with xyz is an element of I - phi(I), then either xy is an element of I or z is an element of I. In addition to give many properties and characterizations of phi-1-absorbing prime ideals, we also determine rings in which every proper ideal is phi-1-absorbing prime.