A representation theorem for integral rigs and its applications to residuated lattices

We generalize the Dubuc–Poveda representation theorem for MV-algebras so that it applies to other algebraic categories of residuated join-semilattices. In particular, as a corollary, we obtain a representation result for pre-linear residuated join-semilattices in terms of totally ordered fibers. The...

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Autores principales: Castiglioni, José Luis, Menni, Matías, Zuluaga Botero, William Javier
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2016
Materias:
Matemática
Sheaves
Integral rigs
Really local objects
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/99230
https://ri.conicet.gov.ar/11336/54815
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-99230
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Sheaves
Integral rigs
Really local objects
spellingShingle Matemática
Sheaves
Integral rigs
Really local objects
Castiglioni, José Luis
Menni, Matías
Zuluaga Botero, William Javier
A representation theorem for integral rigs and its applications to residuated lattices
topic_facet Matemática
Sheaves
Integral rigs
Really local objects
description We generalize the Dubuc–Poveda representation theorem for MV-algebras so that it applies to other algebraic categories of residuated join-semilattices. In particular, as a corollary, we obtain a representation result for pre-linear residuated join-semilattices in terms of totally ordered fibers. The main result is analogous to the Zariski representation of (commutative) rings and it is proved using tools from topos theory.
format Articulo
Preprint
author Castiglioni, José Luis
Menni, Matías
Zuluaga Botero, William Javier
author_facet Castiglioni, José Luis
Menni, Matías
Zuluaga Botero, William Javier
author_sort Castiglioni, José Luis
title A representation theorem for integral rigs and its applications to residuated lattices
title_short A representation theorem for integral rigs and its applications to residuated lattices
title_full A representation theorem for integral rigs and its applications to residuated lattices
title_fullStr A representation theorem for integral rigs and its applications to residuated lattices
title_full_unstemmed A representation theorem for integral rigs and its applications to residuated lattices
title_sort representation theorem for integral rigs and its applications to residuated lattices
publishDate 2016
url http://sedici.unlp.edu.ar/handle/10915/99230
https://ri.conicet.gov.ar/11336/54815
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