Geodesic
The submaximal clones on the three-element set with finitely many relative R-classes
Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 1, pp. 7-33

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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.
Keywords: clone, maximal clone, submaximal clone, Green 's relations 
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Lehtonen, Erkko; Szendrei, Ágnes. The submaximal clones on the three-element set with finitely many relative R-classes. Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 1, pp. 7-33. http://geodesic.mathdoc.fr/item/DMGAA_2010_30_1_a0/