On ϕ-1-absorbing prime ideals


YILDIZ E., TEKİR Ü. , KOÇ S.

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, vol.62, pp.907-918, 2021 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62
  • Publication Date: 2021
  • Doi Number: 10.1007/s13366-020-00557-w
  • Title of Journal : Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
  • Page Numbers: pp.907-918
  • Keywords: phi-prime ideal, 1-absorbing prime ideal, phi-1-absorbing prime ideal, Generalizations of prime ideal, 2-ABSORBING IDEALS

Abstract

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.