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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Detalles Bibliográficos
Publicado: 2010
Materias:
McNaughton
MV-algebra
Representation
Sheaf
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01680072_v161_n8_p1024_Dubuc
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 paper:paper_01680072_v161_n8_p1024_Dubuc
record_format dspace
spelling paper:paper_01680072_v161_n8_p1024_Dubuc2023-06-08T15:17:12Z Representation theory of MV-algebras 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. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01680072_v161_n8_p1024_Dubuc 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
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.
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
publishDate 2010
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01680072_v161_n8_p1024_Dubuc
http://hdl.handle.net/20.500.12110/paper_01680072_v161_n8_p1024_Dubuc
_version_ 1768542264713281536

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