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


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

ALGEBRA COLLOQUIUM, cilt.30, sa.03, ss.481-492, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 03
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1142/s1005386723000391
  • Dergi Adı: ALGEBRA COLLOQUIUM
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.481-492
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.