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Abstract
AbstractBuilding on similar notions for MV-algebras, polyhedral DMV-algebras are defined and investigated. For such algebras dualities with suitable categories of polyhedra are established, and the relation with finitely presented Riesz MV-algebras is investigated. Via hull-functors, finite products are interpreted in terms of hom-functors, and categories of polyhedral MV-algebras, polyhedral DMV-algebras and finitely presented Riesz MV-algebras are linked together. Moreover, the amalgamation property is proved for finitely presented DMV-algebras and Riesz MV-algebras, and for polyhedral DMV-algebras.
Highlights
One of the main results in the theory of MV-algebras is the so-called Marra-Spada duality
Among all different results on expansions of MV-algebras, what is crucial for this note is the fact that a suitable version of the Marra-Spada duality is proved for both the categories of finitely presented DMV-algebras and finitely presented Riesz MV-algebras
We further prove the amalgamation property for finitely presented DMV-algebras and finitely presented Riesz MV-algebras, as well as for polyhedral DMV-algebras
Summary
One of the main results in the theory of MV-algebras is the so-called Marra-Spada duality. Note that in the Marra-Spada duality κ can be an arbitrary cardinal, possibly infinite, while the algebras obtained by considering (closed) polyhedra in finite-dimensional hypercubes are called polyhedral MV-algebras and they are investigated in [1]. Another major line of research in the framework of MV-algebras stemmed out from a simple remark: the standard example of an MV-algebra – that is the unit interval [0, 1] – is closed with respect to the product of real numbers. Among all different results on expansions of MV-algebras, what is crucial for this note is the fact that a suitable version of the Marra-Spada duality is proved for both the categories of finitely presented DMV-algebras and finitely presented Riesz MV-algebras. We urge the interested reader to consult these references for a more detailed account of the topic
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