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Let R be a conmutative semiring with 0 and 1, and let Spec(R) be the set of all proper prime ideals of R. Spec(R) can be endowed with two topologies,… Click to show full abstract
Let R be a conmutative semiring with 0 and 1, and let Spec(R) be the set of all proper prime ideals of R. Spec(R) can be endowed with two topologies, the Zariski topology and the D-topology. Let Max R denote the set of all maximals prime ideals of R. We prove that the two topologies coincide on Spec(R) and on Max R if and only if R is zero dimensional and Gelfand semiring, respectively.
Keywords:
characterization gelfand;
zero dimensional;
topology;
gelfand zero;
topological characterization
Journal Title: Applied general topology
Year Published: 2018
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Journal Title: Applied general topology
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!