Congruence-preserving functions on Stone and Kleene algebras

Abstract

We investigate local polynomial functions on Stone algebras and on Kleene algebras. We find a generating set for the clone of all local polynomial functions. We also represent local polynomial functions on a given algebra by polynomial functions of some canonical extension of this algebra.

Congruence-preserving functions on distributive lattices

“…This paper came with the idea that local polynomial functions might be described as polynomials in a suitable extension of a given algebra. This idea has been further developed in [11] for the cases of Stone and Kleene algebras. In our present paper it is the key to the solution of the above Problems for all (in general unbounded) distributive lattices.…”