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Archimedean positively ordered semigroups with maximal elements

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Abstract

We prove that for every archimedean positively ordered semigroup \(S\) with a maximal element, if \(S\) satisfies one minor condition, then \(S\) is isomorphic to a mixture of \(P_1\) and \(P_1^*\) in the notation of [2]. We also discuss a variation of metrizable spaces where we use a positively ordered semigroup to describe distances.

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Acknowledgements

The author thanks Miami University for support via the faculty research grant program.

He is also grateful to the anonymous referee for helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Miami University, 301 S. Patterson Ave., Oxford, Ohio, 45056, USA

    Tetsuya Ishiu

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  1. Tetsuya Ishiu
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Correspondence to Tetsuya Ishiu.

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Communicated by Jimmie D. Lawson.

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Ishiu, T. Archimedean positively ordered semigroups with maximal elements. Semigroup Forum 105, 244–264 (2022). https://doi.org/10.1007/s00233-022-10297-z

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