A subclass of Ockham algebras

Here we introduce a subclass of the class of Ockham algebras (L; f) for which L satisfies the property that for every x ∈ L, there exists n ≥ 0 such that f ⁿ (x) and f ⁿ⁺¹(x) are complementary. We characterize the structure of the lattice of congruences on such an algebra (L; f). We show that the lattice of compact congruences on L is a dual Stone lattice, and in particular, that the lattice Con L of congruences on L is boolean if and only if L is finite boolean. We also show that L is congruence coherent if and only if it is boolean. Finally, we give a sufficient and necessary condition to have the subdirectly irreducible chains.