Artículo
Dubuc, E.J.; Poveda, Y.A. "Representation theory of MV-algebras" (2010) Annals of Pure and Applied Logic. 161(8):1024-1046
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | Representation theory of MV-algebras |
| Autor: | Dubuc, E.J.; Poveda, Y.A. |
| Filiación: | Departamento de Matematicas, F.C.E. y N., UBA, Buenos Aires, Argentina Departamento de Matematicas, Universidad Tecnologica de Pereira, Pereira, Colombia |
| Palabras clave: | McNaughton; MV-algebra; Representation; Sheaf |
| Año: | 2010 |
| Volumen: | 161 |
| Número: | 8 |
| Página de inicio: | 1024 |
| Página de fin: | 1046 |
| DOI: | http://dx.doi.org/10.1016/j.apal.2009.12.006 |
| Título revista: | Annals of Pure and Applied Logic |
| Título revista abreviado: | Ann. Pure Appl. Logic |
| ISSN: | 01680072 |
| CODEN: | APALD |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01680072_v161_n8_p1024_Dubuc |
Referencias:
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- Poveda, Y., (2007), Una Teoria General de Representacion para MV-algebras, Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales; Yang, Y.C., (2006), http://elib.uni-stuttgart.de/opus/volltexte/2006/2508, l-Groups and Bezout Domains, Von der Fakultat Math. und Physik der Universitat Stuttgart
Citas:
---------- APA ----------
Dubuc, E.J. & Poveda, Y.A. (2010) . Representation theory of MV-algebras. Annals of Pure and Applied Logic, 161(8), 1024-1046.http://dx.doi.org/10.1016/j.apal.2009.12.006
---------- CHICAGO ----------
Dubuc, E.J., Poveda, Y.A. "Representation theory of MV-algebras" . Annals of Pure and Applied Logic 161, no. 8 (2010) : 1024-1046.http://dx.doi.org/10.1016/j.apal.2009.12.006
---------- MLA ----------
Dubuc, E.J., Poveda, Y.A. "Representation theory of MV-algebras" . Annals of Pure and Applied Logic, vol. 161, no. 8, 2010, pp. 1024-1046.http://dx.doi.org/10.1016/j.apal.2009.12.006
---------- VANCOUVER ----------
Dubuc, E.J., Poveda, Y.A. Representation theory of MV-algebras. Ann. Pure Appl. Logic. 2010;161(8):1024-1046.http://dx.doi.org/10.1016/j.apal.2009.12.006
