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Clones with finitely many relative R-classes

Lehtonen, Erkko; Szendrei, Ágnes

Algebra Universalis, 65 (2011), 109-159

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 clones for which there are only finitely many relative R-classes.