Abstract
This study aims to investigate the Zariski topology on the prime ideals of a commutative semigroup S, denoted by Spec(S). First, we show that a topological space X is homeomorphic to Spec(S) for some commutative semigroup S if and only if X is an SS-space that can be described purely in topological terms. Next, we show that an adjunction exists between the category of commutative semigroups and that of SS-spaces. We further show that the category of commutative idempotent semigroups is dually equivalent to that of SS-spaces.
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We would like to thank the anonymous referees for the careful reading and valuable comments which have improved the quality of this paper.
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Communicated by Marcel Jackson.
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Supported by National Natural Science Foundation of China (No. 11771134).
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Wu, H., Li, Q. On the spectra of commutative semigroups. Semigroup Forum 101, 465–485 (2020). https://doi.org/10.1007/s00233-020-10119-0
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DOI: https://doi.org/10.1007/s00233-020-10119-0