The submaximal clones on the three-element set with finitely many relative R-classes
Erkko Lehtonen, Ágnes Szendrei (2010)
Discussiones Mathematicae - General Algebra and Applications
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For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.