Abstract
The variety pOconsists of those algebras (L;⋁,⋀,f,*,0,1) where (L;⋁,⋀,f,0,1) is an Ockham algebra, (L;⋁,⋀,f,*,0,1) is a p-algebra, and the unary operations fand *. commute. For an algebra in pK ωwe show that the compact congruences form a dual Stone lattice and use this to determine necessary and sufficient conditions for a principal congruence to be complemented. We also describe the lattice of subvarieties of pK 1,1identifying therein the biggest subvariety in which every principal congruence is complemented, and the biggest subvariety in which the intersection of two principal congruences is principal.
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