Simple semirings with a bi-absorbing element

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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Correspondence to Miroslav Korbelář.

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

Communicated by Laszlo Marki.

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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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Keywords

  • Simple semiring
  • Bi-absorbing
  • Semimodule
  • Idempotent
  • Semilattice