The algebra of binary trees is affine complete
- MathematicsDiscret. Math. Theor. Comput. Sci.
It is shown that on the algebra of 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.
Congruence preserving functions on free monoids
A function on an algebra is congruence preserving if for any congruence, it maps congruent elements to congruent elements. We show that on a free monoid generated by at least three letters, a…
Galois Connections for Operations and Relations
This paper reports on various Galois connections between operations and relations. Several specifications and generalizations are discussed.
AFFINE COMPLETE ALGEBRAS ABSTRACTING KLEENE AND STONE ALGEBRAS
Boolean algebras are affine complete by a well-known result of G. Grätzer. Various generalizations of this result have been obtained. Among them, a characterization of affine complete Stone algebras…
On affine completeness of distributive p-algebras
- MathematicsGlasgow Mathematical Journal
G. Grätzer in  proved that any Boolean algebra B is affine complete, i.e. for every n ≥ 1, every function f:Bn→B preserving the congruences of B is algebraic. Various generalizations of this…
Affine complete double Stone algebras with bounded core
For geometrical-reasons, H. Werner  called an algebra A a/fine complete if it has the property that for every integer n---1, every function [ : A"---~ A that preserves the congruences of A is…
Über kompatible Funktionen in universalen Algebren
Über die affin vollständigen, endlich erzeugbaren Moduln
A universal algebraA is calledk-affine complete, if any function of the Cartesian powerAk intoA, which is compatible with all congruence relations ofA, is a polynomial function.A is called affine…