2020/05/18 by André Arnold, Arnold, A., Patrick Cégielski +5
Computer Science · #06A99 #08A30 #08B20 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2006.04540
openalex publication_date 2020/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of complete 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. This exhibits an example of a non commutative and non associative affine complete algebra. As far as we know, it is the first example of such an algebra.