The lattice of subvarieties of the biregularization of the variety of Boolean algebras

Abstract

Let τ : F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity ϕ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by V b the biregularization of V , i.e. the variety of type τ defined by all biregular identities from Id (V ).Let B be the variety of Boolean algebras of type τ b : {+, ·, } → N , where τ b (+) = τ b (·) = 2 and τ b ( ) = 1. In this paper we characterize the lattice L(B b ) of all subvarieties of the biregularization of the variety B.