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Dense Relations Are Determined by Their Endomorphism Monoids

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Abstract

We introduce the class of dense relations on a set X and prove that for any finitary or infinitary dense relation ρ on X, the relational system (X,ρ) is determined up to semi-isomorphism by the monoid End(X,ρ) of endomorphisms of (X,ρ). In the case of binary relations, a semi-isomorphism is an isomorphism or an anti-isomorphism.

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Authors and Affiliations

  1. Universidade Aberta and CAUL R. Escola Politecnica, 147 1269-001 Lisboa, Portugal

    João Araújo

  2. University of Mary Washington, Department of Mathematics, Fredericksburg, VA 22401, USA

    Janusz Konieczny

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  1. João Araújo
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  2. Janusz Konieczny
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Correspondence to João Araújo or Janusz Konieczny.

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Araújo, J., Konieczny, J. Dense Relations Are Determined by Their Endomorphism Monoids. Semigroup Forum 70, 302–306 (2005). https://doi.org/10.1007/s00233-004-0164-7

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  • DOI: https://doi.org/10.1007/s00233-004-0164-7

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