Characterizations of biselective operations

  • J. Devillet
  • G. KissEmail author


Let X be a nonempty set and let \({i, j \in \{1, 2, 3, 4\}}\). We say that a binary operation \({F \colon X ^{2} \to X}\) is (i, j)-selective if
$$F(F(x_1, x_2), F(x_3, x_4)) = F(x_i, x_j),$$
for all \({x_1, x_2, x_3, x_4 \in X}\). In this paper we provide characterizations of the class of (i, j)-selective operations. We also investigate some subclasses by adding algebraic properties such as associativity or bisymmetry.

Key words and phrases

(i, j)-selectiveness transitivity axiomatization associativity bisymmetry 

Mathematics Subject Classification

primary 39B52 


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The authors thank the reviewer for quick and careful review and useful suggestions. They also thank Jean-Luc Marichal for fruitful discussions and valuable remarks.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Mathematics Research UnitUniversity of LuxembourgEsch-sur-AlzetteLuxembourg
  2. 2.Alfréd Rényi Institute of MathematicsHungarian Academy of ScienceBudapestHungary

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