More covers of the Boolean variety of unital ℓ-groups

Abstract

Within the lattice of varieties of pseudo MV-algebras, the variety \({\mathcal{B}}\) of Boolean algebras is the least nontrivial variety. Komori identified all varieties of (commutative) MV-algebras that cover \({\mathcal{B}}\) . The authors previously identified all solvable varieties of pseudo MV-algebras that cover \({\mathcal{B}}\) . We will show the existence of continuum many nonsolvable varieties of pseudo MV-algebras that cover \({\mathcal{B}}\), show that periodically primitive ul-groups cannot generate Boolean covers, and show that all noncommutative varieties that are Boolean covers must be Top Boolean.