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Characterizations of quasitrivial symmetric nondecreasing associative operations

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Abstract

We provide a description of the class of n-ary operations on an arbitrary chain that are quasitrivial, symmetric, nondecreasing, and associative. We also prove that associativity can be replaced with bisymmetry in the definition of this class. Finally we investigate the special situation where the chain is finite.

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Acknowledgements

The authors would like to thank Bruno Teheux for fruitful discussions and valuable remarks. This research is supported by the Internal Research Project R-AGR-0500 of the University of Luxembourg and the Luxembourg National Research Fund R-AGR-3080. The second author is also supported by the Hungarian National Foundation for Scientific Research, Grant No. K124749.

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Authors and Affiliations

  1. Mathematics Research Unit, University of Luxembourg, Maison du Nombre, 6, Avenue de la Fonte, 4364, Esch-sur-Alzette, Luxembourg

    Jimmy Devillet & Jean-Luc Marichal

  2. Alfred Renyi Institute of Mathematics, Hungarian Academy of Science, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Gergely Kiss

Authors
  1. Jimmy Devillet
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  2. Gergely Kiss
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  3. Jean-Luc Marichal
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Correspondence to Jean-Luc Marichal.

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Communicated by Mikhail Volkov.

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Devillet, J., Kiss, G. & Marichal, JL. Characterizations of quasitrivial symmetric nondecreasing associative operations. Semigroup Forum 98, 154–171 (2019). https://doi.org/10.1007/s00233-018-9980-z

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  • DOI: https://doi.org/10.1007/s00233-018-9980-z

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