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dc.contributor.author
Dubuc, Eduardo Julio
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dc.contributor.author
Poveda, Y. A.
dc.date.available
2017-07-04T15:34:52Z
dc.date.issued
2015-08
dc.identifier.citation
Dubuc, Eduardo Julio; Poveda, Y. A.; On the equivalence between MV-algebras and l-groups with strong unit; Springer; Studia Logica; 103; 4; 8-2015; 807-814
dc.identifier.issn
0039-3215
dc.identifier.uri
http://hdl.handle.net/11336/19451
dc.description.abstract
In “A new proof of the completeness of the Lukasiewicz axioms” (Trans Am Math Soc 88, 1959) Chang proved that any totally ordered MV -algebra A was isomorphic to the segment A ∼= Γ(A∗, u) of a totally ordered l-group with strong unit A∗. This was done by the simple intuitive idea of putting denumerable copies of A on top of each other (indexed by the integers). Moreover, he also show that any such group G can be recovered from its segment since G ∼= Γ(G, u) ∗, establishing an equivalence of categories. In “Interpretation of AF C∗-algebras in Lukasiewicz sentential calculus” (J Funct Anal 65, 1986) Mundici extended this result to arbitrary MV -algebras and l-groups with strong unit. He takes the representation of A as a sub-direct product of chains Ai, and observes that A → i Gi where Gi = A∗ i . Then he let A∗ be the l-subgroup generated by A inside i Gi. He proves that this idea works, and establish an equivalence of categories in a rather elaborate way by means of his concept of good sequences and its complicated arithmetics. In this note, essentially self-contained except for Chang’s result, we give a simple proof of this equivalence taking advantage directly of the arithmetics of the the product l-group i Gi, avoiding entirely the notion of good sequence.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Mv Algebras
dc.subject
L Groups
dc.subject
Good Sequences
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
On the equivalence between MV-algebras and l-groups with strong unit
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-06-26T14:06:41Z
dc.identifier.eissn
1572-8730
dc.journal.volume
103
dc.journal.number
4
dc.journal.pagination
807-814
dc.journal.pais
Países Bajos
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dc.journal.ciudad
Dordrecht
dc.description.fil
Fil: Dubuc, Eduardo Julio. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.description.fil
Fil: Poveda, Y. A.. Universidad Tecnológica de Pereira; Colombia
dc.journal.title
Studia Logica
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s11225-014-9593-9
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs11225-014-9593-9
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1408.1070
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