On the geometric theory of local MV-algebras
| Autor: | Olivia Caramello, Anna Carla Russo |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Representation theorem 010102 general mathematics Classifying topos Geometric logic Grothendieck topology Lattice-ordered abelian group Local MV-algebra Morita-equivalence Theory of presheaf type Presheaf 0102 computer and information sciences 01 natural sciences Geometric group theory 010201 computation theory & mathematics 0101 mathematics Morita equivalence Abelian group Variety (universal algebra) Quotient Mathematics |
| Zdroj: | Journal of Algebra. 479:263-313 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2017.01.005 |
| Popis: | We investigate the geometric theory of local MV-algebras and its quotients axiomatizing the local MV-algebras in a given proper variety of MV-algebras. We show that, whilst the theory of local MV-algebras is not of presheaf type, each of these quotients is a theory of presheaf type which is Morita-equivalent to an expansion of the theory of lattice-ordered abelian groups. Di Nola–Lettieri's equivalence is recovered from the Morita-equivalence for the quotient axiomatizing the local MV-algebras in Chang's variety, that is, the perfect MV-algebras. We establish along the way a number of results of independent interest, including a constructive treatment of the radical for MV-algebras in a fixed proper variety of MV-algebras and a representation theorem for the finitely presentable algebras in such a variety as finite products of local MV-algebras. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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