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 having a smallest dense element was given by R. Beazer. In this paper, generalizations of Beazer’s result are presented for algebras abstracting simultaneously Kleene and Stone algebras.

Abstract. An algebra is called affine complete if all its compatible (i.e. congruence-preserving) functions are polynomial functions. In this paper we characterize affine complete members in the… Expand

In [1] R. Beazer characterized affine complete Stone algebras having a smallest dense element. We remove this latter assumption and describe affine complete algebras in the class of all Stone… Expand

G. Grätzer in [4] 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… Expand

Proceedings of the Royal Society of Edinburgh: Section A Mathematics

1983

Synopsis We consider a common abstraction of de Morgan algebras and Stone algebras which we call an MS-algebra. The variety of MS-algebras is easily described by adjoining only three simple equations… Expand

Proceedings of the Royal Society of Edinburgh: Section A Mathematics

1983

Synopsis In a previous publication (1983), we defined a class of algebras, denoted by MS, which generalises both de Morgan algebras and Stone algebras. Here we describe the lattice of subvarieties of… Expand

The first construction of MS-algebras from Kleene algebras and distributive lattices was presented by T.S. Blyth and J.C. Varlet in [3]. This was a construction by means of so-called “triples” which… Expand