LOCAL POLYNOMIAL FUNCTIONS ON ALGEBRAS GENERALIZING STONE AND KLEENE ALGEBRAS

ABSTRACT: An n-ary function on an algebra A is said to be a local polynomial function of A if it can be interpolated by a polynomial of A on every finite subset of A^n. A description of local polynomial functions of algebras from a given variety is important when characterizing locally affine complete members of this variety. We describe local polynomial functions of de Morgan algebras as compatible functions preserving a certain binary relation. Also, we present some results about local polynomial functions of K_2-algebras.