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Convergence in MV-algebras
dc.contributor.author | Georgescu, George |
dc.contributor.author | Liguori, Fortuna |
dc.contributor.author | Martini, Giulia |
dc.date.accessioned | 2007-09-14T10:28:10Z |
dc.date.available | 2007-09-14T10:28:10Z |
dc.date.issued | 1997 |
dc.identifier.issn | 1134-5632 |
dc.identifier.uri | http://hdl.handle.net/2099/3484 |
dc.description.abstract | $MV$-algebras were introduced in 1958 by Chang and they are models of Lukasiewicz infinite-valued logic. Chang gives a correspondence between the category of linearly ordered $MV$-algebras and the category of linearly ordered abelian $\ell$-groups. Mundici extended this result showing a categorical equivalence between the category of the $MV$-algebras and the category of the abelian $\ell$-groups with strong unit. In this paper, starting from some definitions and results in abelian $\ell$-groups, we shall study the convergent sequences and the Cauchy sequences in an $MV$-algebra. The main result is the construction of the Cauchy completion $A^{*}$ of an $MV$-algebra $A$. It is proved that a complete $MV$-algebra is also Cauchy complete. Additional results on atomic and complete $MV$-algebras are also given. |
dc.format.extent | 41-52 |
dc.language.iso | eng |
dc.publisher | Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica |
dc.relation.ispartof | Mathware & soft computing . 1997 Vol. 4 Núm. 1 |
dc.rights | Reconeixement-NoComercial-CompartirIgual 3.0 Espanya |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject.other | Complete MV-algebras |
dc.title | Convergence in MV-algebras |
dc.type | Article |
dc.subject.lemac | Lògica algebraica |
dc.subject.lemac | Anells commutatius |
dc.subject.ams | Classificació AMS::03 Mathematical logic and foundations::03G Algebraic logic |
dc.rights.access | Open Access |
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1997, Vol. IV, Núm. 1 [6]
"MV-algebras (part II)"