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Tight inverse semigroups that are not bisimple

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A semigroup is tight if each of its congruences is uniquely determined by eachof the congruence classes. Bisimple inverse semigroups are tight, and tightsemigroups are either simple or congruence-free with zero. Although congruence-freesemigroups are tight, they are not necessarily bisimple. We constructtight inverse semigroups and tight inverse monoids that are neither bisimplenor congruence-free.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Arkansas, 72701, Fayetteville, AR, USA

    Boris M. Schein & H. Y. Wu

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  1. Boris M. Schein
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  2. H. Y. Wu
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Correspondence to Boris M. Schein or H. Y. Wu.

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Communicated by Thomas E. Hall

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Schein, B.M., Wu, H.Y. Tight inverse semigroups that are not bisimple. Semigroup Forum 67, 432–442 (2003). https://doi.org/10.1007/s00233-002-0002-8

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  • DOI: https://doi.org/10.1007/s00233-002-0002-8

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