Some results concerning uniformly (1-absorbing) primary ideals

Alhazmy K., Almahdi F. A. A., Bouba E. M., Koç S.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.2025, pp.1-15, 2025 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 2025
  • Publication Date: 2025
  • Doi Number: 10.1142/s0219498826501902
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1-15
  • Marmara University Affiliated: No

Abstract

Let R be a commutative ring with 1≠0. A proper ideal I of R is said to be a uniformly 1-absorbing primary if there exits a fixed n ∈ ℕ and whenever abc ∈ I for some nonunits a,b,c ∈ R then ab ∈ I or cn ∈ I. In addition to give various properties of uniformly 1-absorbing primary ideals, we characterize some important classes of rings such as von Neumann regular rings, UN-rings, nonlocal rings, fields and divided rings in terms of uniformly 1-absorbing primary ideals. Also, we investigate uniformly primary ideals and uniformly 1-absorbing primary ideals of amalgamated algebras R⋈fJ.