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

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 ${\displaystyle V_b}$ 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 ${\displaystyle {\tau }_b:\{+,·,´\}\to N}$, where ${\displaystyle {\tau }_b(+)={\tau }_b(·)=2}$ and ${\displaystyle {\tau }_b(´)=1}$. In this paper we characterize the lattice ${\displaystyle ℒ\left(B_b\right)}$ of all subvarieties of the biregularization of the variety B.