05902465

j

05902465 Lehtonen, Erkko Szendrei, \'Agnes The submaximal clones on the three-element set with finitely many relative ${\cal R}$-classes. Discuss. Math., Gen. Algebra Appl. 30, No. 1, 7-33 (2010). 2010 University of Zielona G\'ora Press, Zielona G\'ora EN clone maximal clone submaximal clone Green's relations

doi:10.7151/dmgaa.1160

Summary: For each clone ${\cal C}$ on a set $A$ there is an associated equivalence relation analogous to Green's ${\cal R}$-relation, which relates two operations on $A$ if and only if each one is a substitution instance of the other using operations from ${\cal C}$. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative ${\cal R}$-classes.