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 Títol: Convergence in MV-algebras Autor: Georgescu, George; Liguori, Fortuna; Martini, Giulia Editorial: Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica Tipus de document: Article Resum: $MV$-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. ISSN: 1134-5632 URI: http://hdl.handle.net/2099/3484 Apareix a les col·leccions: 1997, Vol. IV, Núm. 1 Comparteix: