Locally s-prime ideals
Comptes Rendus de L'Academie Bulgare des Sciences, vol.73, no.12, pp.1650-1657, 2020 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 73 Issue: 12
- Publication Date: 2020
- Doi Number: 10.7546/crabs.2020.12.03
- Journal Name: Comptes Rendus de L'Academie Bulgare des Sciences
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, zbMATH
- Page Numbers: pp.1650-1657
- Keywords: Locally s-prime ideal, S-Noetherian ring
- Istanbul Gelisim University Affiliated: No
Abstract
Let R be a commutative ring and S be a multiplicatively closed subset of R. A proper ideal P of R is called locally S-prime if PSis a prime ideal of RS. It is shown that, P is a locally S-prime ideal if and only if whenever P ∩ S = Ø and if ab ∈ P for some a; b ∈ R, then there exists s ∈ S such that sa ∈ P or sb ∈ P. As a consequence of this fact and well-known properties of prime ideals we obtain some properties of these ideals. Also, all multiplicatively closed subsets S of R that an ideal can be locally S-prime are characterised. Finally, these ideals are studied in an S-Noetherian ring.