On S-integral domains and S-version of Krull intersection theorem
Abstract
Let S ⊆ R be a multiplicatively closed subset of a ring R. We extend several results on integral domains to their S-versions and establish the S-version of Krull intersection theorem. We also show that if R is an S-field, then the localization of R with respect to S is a ϕ(S)-field, where ϕ(S) ={s/1| s ∈ S} is a multiplicatively closed subset of S^{-1} R, and prove the converse under the condition of finiteness of S. As a consequence, we show that every finite S-integral domain is an S-field. Also, we provide several examples to illustrate the significance of our findings.
Fields of Study & Subjects
Rings
Modules
and Algebras
Commutative Algebra and Its Applications
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Filomat
- Volume
- 40
- Issue
- 3
- Pages
- 1033–1044
- Publication date
- 1 January 2026
- Language
- EN