Affine completeness of some free binary algebras

• Autorzy: Arnold André , Cégielski Patrick , Guessarian Irène
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

mathematics; rings and Algebras; computer science; formal languages and automata theory

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2022
• Tom: Vol. 186, nr 1-4
• Strony: 27--44
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Arnold André

• Université de Bordeaux, France,

autor

Cégielski Patrick

• LACL Universit´e Paris-Est Cr´eteil – IUT de S´enart-Fontainebleau, France

autor

Guessarian Irène

• IRIF, CNRS & Universit´e Paris-Diderot, Emerita Sorbonne Universit´e, France

Bibliografia

• [1] Arnold A., Cégielski P., Grigorieff S., Guessarian I.: Affine completeness of the algebra of full binary trees. Algebra Universalis, 2020. Springer Verlag, 81: 55. doi:10.1007/s00012-020-00690-6
• [2] Cégielski, P., Grigorieff, S., Guessarian, I.: Newton representation of functions over natural integers having integral difference ratios. International Journal of Number Theory, 2015. 11 (7): 2019–2139. doi: 10.1142/S179304211550092X.
• [3] Cégielski P., Grigorieff S., Guessarian I.: Congruence preserving functions on free monoids. Algebra Universalis, 2017. 78 (3), 389–406. doi:DOI: 10.1007/s00012-017-0464-x.
• [4] Kaarli K., Pixley A.F.: Polynomial Completeness in Algebraic Systems. Chapman & Hall/CRC (2001)
• [5] Nöbauer W.: Affinvollst¨andige Moduln. Mathematische Nachrichten, 1978. 86: 85–96. doi:10.1002/mana.19780860110.
• [6] Ploščica M., Haviar M.: Congruence-preserving functions on distributive lattices. Algebra Universalis, 2008. 59 (1): 179–196. doi: 10.1007/s00012-008-2099-4.
• [7] Werner H.: Produkte von KongruenzKlassengeometrien universeller Algebren. Math. Zeitschrift, 1971. 121(2), 111–140. doi:10.1007/BF01113481.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023). (PL)