The spectrum problem for $\ell$-groups and for MV-algebras: a categorical approachAs a main result, we characterize prime spectra of abelian lattice ordered
groups. Further we introduce some categories based on spectral spaces, lattices
and Priestley spaces, and we relate these categories with each other and with
the category of presented MV-algebras, by means of functors. We turn to
lattices and offer a simple characterization of 1) maps whose Stone dual
preserves closed sets, and 2) closed epimorphisms between distributive lattices
as well as their Stone duals. We have a characterization of the variety
generated by the Chang MV-algebra and we study this variety. Next we generalize
the results to every variety generated by a Komori chain. Finally we discuss
homogeneous polynomials in MV-algebras.
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