Covers of the Abelian Variety of Generalized MV-Algebras

Using the categorical equivalence of the class of generalized MV-algebras with the class of unital ℓ-groups, we describe all varieties of symmetric top abelian unital ℓ-groups that cover the variety 𝒜 uℓ of abelian unital ℓ-groups. Equivalently, we describe all cover varieties of the variety of MV-algebras, ℳ𝒱, within the variety of generalized MV-algebras admitting only one negation and each of whose maximal ideals is normal. In particular, there are continuum many representable varieties of generalized MV-algebras that cover ℳ𝒱.

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