On ϕ - ( n,N ) -ideals of Commutative Rings

Anebri A., Mahdou N., Tekir Ü., Yıldız E.

ALGEBRA COLLOQUIUM, vol.30, no.03, pp.481-492, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 03
  • Publication Date: 2023
  • Doi Number: 10.1142/s1005386723000391
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.481-492
  • Yıldız Technical University Affiliated: Yes


Let [Formula: see text] be a commutative ring with nonzero identity and [Formula: see text] be a positive integer. In this paper, we introduce and investigate a new subclass of [Formula: see text]-[Formula: see text]-absorbing primary ideals, which are called [Formula: see text]-[Formula: see text]-ideals. Let [Formula: see text] be a function, where [Formula: see text] denotes the set of all ideals of [Formula: see text]. A proper ideal [Formula: see text] of [Formula: see text] is called a [Formula: see text]-[Formula: see text]-ideal if [Formula: see text] and [Formula: see text] imply that the product of [Formula: see text] with [Formula: see text] of [Formula: see text] is in [Formula: see text] for all [Formula: see text]. In addition to giving many properties of [Formula: see text]-[Formula: see text]-ideals, we also use the concept of [Formula: see text]-[Formula: see text]-ideals to characterize rings that have only finitely many minimal prime ideals.