2-absorbing phi-delta-primary ideals

Yavuz S., Onar S., Ersoy B. A. , Tekir Ü., Koç S.

TURKISH JOURNAL OF MATHEMATICS, vol.45, no.5, pp.1927-1939, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2105-21
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1927-1939
  • Keywords: 2-absorbing ideal, 2-absorbing primary ideal, 2-absorbing phi-delta-primary ideal

Abstract

This paper aims to introduce 2-absorbing phi-delta-primary ideals over commutative rings which unify the concepts of all generalizations of 2-absorbing and 2-absorbing primary ideals. Let A be a commutative ring with a nonzero identity and I(A) be the set of all ideals of A. Suppose that delta : I(A) -> I(A) is an expansion function and phi : I(A) -> I(A)U{theta} is a reduction function. A proper ideal Q of A is said to be a 2-absorbing phi-delta-primary if whenever abc is an element of Q - phi(Q), where a, b, c is an element of R, then either ab is an element of Q or ac is an element of delta(Q) or bc is an element of delta(Q). Various examples, properties, and characterizations of this new class of ideals are given.