On S-Zariski topology
Eda Yıldız, Bayram Alì Ersoy, Ünsal Teki̇̀r, Suat Koç
Abstract
Let R be a commutative ring with nonzero identity and, S⊆R be a multiplicatively closed subset. An ideal P of R with P∩S=∅ is called an S-prime ideal if there exists an (fixed) s∈S and whenver ab∈P for a,b∈R then either sa∈P or sb∈P. In this article, we construct a topology on the set SpecS(R) of all S-prime ideals of R which is generalization of prime spectrum of R. Also, we investigate the relations between algebraic properties of R and topological properties of SpecS(R) like compactness, connectedness and irreducibility.
Topics & Concepts
MathematicsPrime (order theory)Ideal (ethics)Commutative ringIrreducibilityAssociated primeSocial connectednessPrime idealTopology (electrical circuits)GeneralizationSpectrum (functional analysis)Discrete mathematicsCombinatoricsCommutative propertyPure mathematicsEpistemologyMathematical analysisPhysicsPsychotherapistPhilosophyQuantum mechanicsPsychologyRings, Modules, and AlgebrasAdvanced Topics in AlgebraAlgebraic structures and combinatorial models