Varieties of Regular Pseudocomplemented de Morgan Algebras

In this paper, we investigate the varieties M_n and K_n of regular pseudocomplemented de Morgan and Kleene algebras of range n, respectively. Priestley duality as it applies to pseudocomplemented de Morgan algebras is used. We characterise the dual spaces of the simple (equivalently, subdirectly irreducible) algebras in M_n and explicitly describe the dual spaces of the simple algebras in M₁ and K₁. We show that the variety M₁ is locally finite, but this property does not extend to M_n or even K_n for n =?2. We also show that the lattice of subvarieties of K₁ is an ? +?1 chain and the cardinality of the lattice of subvarieties of either K₂ or M₁ is 2^?. A description of the lattice of subvarieties of M₁ is given.