Congruences on Ockham algebras with pseudocomplementation

The variety pO consists of those algebras (L Lambda, V, f, *, 0, 1) where ( L; Lambda, V, f, 0, 1) is an Ockham algebra, (L; Lambda, V, *, 0, 1) is a p -algebra, and the unary operations f and * commute. For an algebra in pK(om ega) we show that the compact congruences Form a dual Stone lattice and use this to determine necessary and sufficient conditions for a principal cong ruence to be complemented. W also describe the lattice of subvarieties of p K(1,1), identifying therein the biggest subvariety in which every principal congruence is complemented, and the biggest subvariety in which the inters ection of two principal congruences is principal.