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Congruence preserving functions on median algebras. (English) Zbl 1234.08005
Chajda, I. (ed.) et al., Proceedings of the 79th workshop on general algebra “79. Arbeitstagung Allgemeine Algebra”, 25th conference of young algebraists, Palacký University Olomouc, Olomouc, Czech Republic, February 12–14, 2010. Klagenfurt: Verlag Johannes Heyn (ISBN 978-3-7084-0407-3/pbk). Contributions to General Algebra 19, 179-186 (2010).
In a previous paper of the present author and M. Haviar [Algebra Univers. 59, No. 1–2, 179–196 (2008; Zbl 1178.06006)], the structure of the clone of all congruence-preserving finitary functions on a distributive lattice was clarified. Since median algebras are intrinsically related to distributive lattices, an analogous structural analysis of the clone of all congruence-preserving finitary functions on a median algebra should be feasible. The present paper contributes to this endeavor: Unary congruence-preserving functions are shown to be compositions of polynomials, certain complementations, and special projections; for finitary functions in general, a plausible analogous conjecture is proposed without proof.
For the entire collection see [Zbl 1201.08001].
08A30 Subalgebras, congruence relations
06B10 Lattice ideals, congruence relations
08A40 Operations and polynomials in algebraic structures, primal algebras