Affiliations: [a] Université de Bordeaux, France, [email protected]
| [b] LACL, Université Paris-Est Créteil – IUT de Sénart-Fontainebleau, France, [email protected]
| [c] IRIF, CNRS & Université Paris-Diderot, Emerita Sorbonne Université, France, [email protected]
Correspondence:
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Address of correspondence: IRIF, CNRS & Université Paris-Diderot, Emerita Sorbonne Université, France
Abstract: A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. An algebra is said to be affine complete if every congruence preserving function is a polynomial function. We show that the algebra of (possibly empty) binary trees whose leaves are labeled by letters of an alphabet containing at least one letter, and the free monoid on an alphabet containing at least two letters are affine complete.
