Commuting double Ockham algebras

In this paper, we study a certain class of double Ockham algebras (L; ∧, ∨, f, k, 0, 1), namely the bounded distributive lattices (L; ∧, ∨, 0, 1) endowed with a commuting pair of unary operations f and k, both of which are dual endomorphisms. We characterize the subdirectly irreducible members, and also consider the special case when both (L; f) and (L; k) are de Morgan algebras. We show via Priestley duality that there are precisely nine non-isomorphic subdirectly irreducible members, all of which are simple.