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

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