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Affine Completeness of Some Free Binary Algebras

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.
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https://hal-cnrs.archives-ouvertes.fr/hal-03774320
Contributor : irene guessarian Connect in order to contact the contributor
Submitted on : Saturday, September 10, 2022 - 10:26:01 AM
Last modification on : Monday, September 12, 2022 - 3:40:39 AM

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André Arnold, Patrick Cégielski, Irène Guessarian. Affine Completeness of Some Free Binary Algebras. Fundamenta Informaticae, Polskie Towarzystwo Matematyczne, 2022, 186 (1-4), pp.27-44. ⟨10.3233/FI-222117⟩. ⟨hal-03774320⟩

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