Characterizations of biselective operations

Devillet, Jimmy and Kiss, Gergely (2019) Characterizations of biselective operations. ACTA MATHEMATICA HUNGARICA, 157 (2). pp. 387-407. ISSN 0236-5294

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Abstract

Let X be a nonempty set and let i,j∈{1,2,3,4} . We say that a binary operation F:X2→X is (i, j)-selective if F(F(x1,x2),F(x3,x4))=F(xi,xj), for all x1,x2,x3,x4∈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.

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