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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Castiglioni, José Luis, Menni, Matías, Zuluaga Botero, William Javier
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2016
Materias:
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/99230
https://ri.conicet.gov.ar/11336/54815
Aporte de:
Descripción
Sumario: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.