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Simple semirings with a bi-absorbing element

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Abstract

We study additively idempotent congruence-simple semirings with a bi-absorbing element. We characterize a subclass of these semirings in terms of semimodules of a special type (o-characteristic semimodules). We show that o-characteristic semimodules are uniquely determined. We also generalize a result by Ježek and Kepka on simple semirings of endomorphisms of semilattices.

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Authors and Affiliations

  1. Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Prague 8, Czech Republic

    Tomáš Kepka

  2. Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27, Prague 6, Czech Republic

    Miroslav Korbelář

  3. Department of Mathematics, Czech University of Life Sciences in Prague, Kamýcká 129, 165 21, Suchdol, Prague 6, Czech Republic

    Petr Němec

Authors
  1. Tomáš Kepka
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  2. Miroslav Korbelář
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  3. Petr Němec
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Corresponding author

Correspondence to Miroslav Korbelář.

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Communicated by Laszlo Marki.

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The second author was supported by the project CAAS CZ.02.1.01/0.0/0.0/16_019/0000778.

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Kepka, T., Korbelář, M. & Němec, P. Simple semirings with a bi-absorbing element. Semigroup Forum 101, 406–420 (2020). https://doi.org/10.1007/s00233-020-10101-w

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  • DOI: https://doi.org/10.1007/s00233-020-10101-w

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