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The endomorphism semiring of a semilattice

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Abstract

We prove that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and describe its monolith. The endomorphism semiring is congruence simple if and only if the semilattice has both a least and a largest element.

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Authors and Affiliations

  1. MFF UK, Sokolovská 83, 18600, Praha 8, Czech Republic

    J. Ježek & T. Kepka

  2. Bolyai Institute, University of Szeged, Szeged, Hungary

    M. Maróti

Authors
  1. J. Ježek
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  2. T. Kepka
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  3. M. Maróti
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Corresponding author

Correspondence to J. Ježek.

Additional information

Communicated by László Márki.

The third author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant nos. T 48809 and K 60148. The work is a part of the research project MSM0021620839 financed by MSMT.

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Ježek, J., Kepka, T. & Maróti, M. The endomorphism semiring of a semilattice. Semigroup Forum 78, 21–26 (2009). https://doi.org/10.1007/s00233-008-9045-9

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  • DOI: https://doi.org/10.1007/s00233-008-9045-9

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