2-absorbing φ-δ-primary ideals

Yavuz S., ONAR S., ERSOY B. A., TEKİR Ü., KOÇ S.

Turkish Journal of Mathematics, vol.45, no.5, pp.1927-1939, 2021 (SCI-Expanded, Scopus, TRDizin) 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 (SCI-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 φ-δ-primary ideal
  • Istanbul Gelisim University Affiliated: No

Abstract

This paper aims to introduce 2-absorbing φ-δ-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 δ: I (A) → I (A) is an expansion function and φ: I (A) → I (A)∪{∅} is a reduction function. A proper ideal Q of A is said to be a 2-absorbing φ-δ-primary if whenever abc ∈ Q − φ (Q), where a, b, c ∈ R, then either ab ∈ Q or ac ∈ δ (Q) or bc ∈ δ (Q). Various examples, properties, and characterizations of this new class of ideals are given.