Abstract :
An abstract algebra 〈A,∧,∨,⊥,⊤,¬,∼〉 is called a De Morgan Boolean algebra if 〈A,∧,∨,⊥,⊤,¬〉 is a Boolean algebra and 〈A,∧,∨,∼〉 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.
Keywords :
Boolean algebra , De Morgan Boolean algebra , De Morgan lattice , Implication , Implicational class , Quasi-identity , Quasivariety , Variety , Subdirectly irreducible algebra , Identity
