On weakly S -prime ideals of commutative rings
On weakly S -prime ideals of commutative rings
Abstract Let R be a commutative ring with identity and S be a multiplicative subset of R . In this paper, we introduce the concept of weakly S -prime ideals which is a generalization of weakly prime ideals. Let P be an ideal of R disjoint with S . We say that P is a weakly S -prime ideal of R if there exists an s ∈ S such that, for all a, b ∈ R , if 0 ≠ ab ∈ P , then sa ∈ P or sb ∈ P . We show that weakly S -prime ideals have many analog properties to these of weakly prime ideals. We also use this new class of ideals to characterize S -Noetherian rings and S -principal ideal rings.
- Universite Moulay Ismail De Meknes Morocco
- King Khalid University Saudi Arabia
- Mohammed V University Morocco
secondary 13b02, 13e99, primary 13a15, QA1-939, nagata idealization, weakly s-prime ideals, s-noetherian rings, s-prime ideals, Mathematics
secondary 13b02, 13e99, primary 13a15, QA1-939, nagata idealization, weakly s-prime ideals, s-noetherian rings, s-prime ideals, Mathematics
3 Research products, page 1 of 1
- 2017IsAmongTopNSimilarDocuments
- 1989IsAmongTopNSimilarDocuments
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).6 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
