Representation theory of MV-algebras

In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-al...

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Autores principales: Dubuc, E.J., Poveda, Y.A.
Formato: JOUR
Materias:
McNaughton
MV-algebra
Representation
Sheaf
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01680072_v161_n8_p1024_Dubuc
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_01680072_v161_n8_p1024_Dubuc
record_format dspace
spelling todo:paper_01680072_v161_n8_p1024_Dubuc2023-10-03T15:05:41Z Representation theory of MV-algebras Dubuc, E.J. Poveda, Y.A. McNaughton MV-algebra Representation Sheaf In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton's theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton's theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. © 2009 Elsevier B.V. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01680072_v161_n8_p1024_Dubuc
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic McNaughton
MV-algebra
Representation
Sheaf
spellingShingle McNaughton
MV-algebra
Representation
Sheaf
Dubuc, E.J.
Poveda, Y.A.
Representation theory of MV-algebras
topic_facet McNaughton
MV-algebra
Representation
Sheaf
description In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton's theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton's theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. © 2009 Elsevier B.V.
format JOUR
author Dubuc, E.J.
Poveda, Y.A.
author_facet Dubuc, E.J.
Poveda, Y.A.
author_sort Dubuc, E.J.
title Representation theory of MV-algebras
title_short Representation theory of MV-algebras
title_full Representation theory of MV-algebras
title_fullStr Representation theory of MV-algebras
title_full_unstemmed Representation theory of MV-algebras
title_sort representation theory of mv-algebras
url http://hdl.handle.net/20.500.12110/paper_01680072_v161_n8_p1024_Dubuc
work_keys_str_mv AT dubucej representationtheoryofmvalgebras
AT povedaya representationtheoryofmvalgebras
_version_ 1782029437623074816

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