Regular doublep-algebras with Stone congruence lattices

Abstract

T h e r e are several results in the l i terature concern ing the charac te r iza t ion of lattices whose congruence lattice is a Stone lattice, See for examp le [4], [5] and [8]. T h e simplest and best known result in this a rea is that for Boo l ean algebras. The congruence lattice of a Boo lean a lgebra is Stone if and only if the a lgebra is comple te . In this note we character ize those regular double p -a lgebras whose congruence lattice is Stone. Examples are given to illustrate the d e p e n d e n c e of o u r results on regulari ty.