Implicational classes of De Morgan Boolean algebras

An abstract algebra [A,boolean AND,boolean OR,perpendicular to,inverted perpendicular,(sic),similar to] is called a De Morgan Boolean algebra if [A,boolean AND,boolean OR,perpendicular to,inverted perpendicular,(sic)] is a Boolean algebra and [A,boolean AND,boolean OR,similar to] is a De Morgan lattice. In this paper we prove that implicational classes of De Morgan Boolean algebras form a four-element chain and are all finitely-axiomatizable and finitely-generated quasivarieties, three of which are varieties. We also show that there are exactly two (up to isomorphism) subdirectly irreducible De Morgan Boolean algebras. (C) 2001 Elsevier Science B.V. All rights reserved.