It is shown that on the algebra of binary trees whose leaves are labeled by letters of an alphabet containing at least three letters, a function is congruence preserving if and only if it is polynomial.Expand

A function on an algebra is congruence preserving if for any congruence, it maps congruent elements to congruent elements. We show that on a free monoid generated by at least three letters, a… Expand

Boolean algebras are affine complete by a well-known result of G. Grätzer. Various generalizations of this result have been obtained. Among them, a characterization of affine complete Stone algebras… Expand

G. Grätzer in [4] proved that any Boolean algebra B is affine complete, i.e. for every n ≥ 1, every function f:Bn→B preserving the congruences of B is algebraic. Various generalizations of this… Expand

For geometrical-reasons, H. Werner [14] called an algebra A a/fine complete if it has the property that for every integer n---1, every function [ : A"---~ A that preserves the congruences of A is… Expand

A universal algebraA is calledk-affine complete, if any function of the Cartesian powerAk intoA, which is compatible with all congruence relations ofA, is a polynomial function.A is called affine… Expand