On weakly <i>S</i> -prime ideals of commutative rings
Fuad Ali Ahmed Almahdi, El Mehdi Bouba, Mohammed Tamekkante
Abstract
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.
Topics & Concepts
Associated primeMathematicsSemiprime ringPrime (order theory)Prime idealBoolean prime ideal theoremIdeal (ethics)Commutative ringNoetherian ringMinimal idealMaximal idealPrime elementPure mathematicsMultiplicative functionGeneralizationFractional idealClass (philosophy)Discrete mathematicsCommutative propertyCombinatoricsComputer scienceLawMathematical analysisArtificial intelligencePolitical scienceRings, Modules, and AlgebrasCommutative Algebra and Its ApplicationsAdvanced Topics in Algebra