Varieties generated by unital Abelian ℓ-groups

Much work has been done on the connections between Abelian ℓ-groups and MV-algebras. For example, it is well known that there is a bijective correspondence between the so-called equational classes of unital Abelian ℓ-groups and the subvarieties of MV, the variety of MV-algebras. The drawback of this correspondence is that these former classes are not varieties. The main result of this paper remedies this situation by establishing that the subvariety lattice of the variety pA of positively-pointed Abelian ℓ-groups (excluding the trivial variety) is isomorphic to the subvariety lattice of MV. In particular, with the exception of the unique atom, every subvariety of pA is generated by its unital members.