Top Varieties of Generalized MV-Algebras and Unital Lattice-Ordered Groups

In spite of the well-know fact that the system of ?-groups with strong unit (unital ?-groups) does not form a variety, there is a categorical connection between the category of unital ?-groups and the variety of generalized MV-algebras which enables us to naturally export equational machinery and terminology like “variety” from the latter category to the former.

Using this categorical equivalence, we study varieties, or equationally defined classes, and top varieties, varieties above the normal valued variety, of both structures. We generalize Chang's Completeness Theorem for generalized MV-algebras, and formulate some open questions for both structures.