Título inglés | Convergence in MV-algebras. |
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Título español | Convergencia en álgebras MV. |
Autor/es | Georgescu, George ; Liguori, Fortuna ; Martini, Giulia |
Organización | Inst. Math., Bucarest, Rumanía;Ist. Mat. Fac. Archit. Univ. Napoli, Nápoles, Italia |
Revista | 1134-5632 |
Publicación | 1997, 4 (1): 41-52, 10 Ref. |
Tipo de documento | articulo |
Idioma | Inglés |
Resumen inglés | MV-algebras were introduced in 1958 by Chang [4] 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 l-groups. Mundici [10] extended this result showing a categorical equivalence between the category of the MV-algebras and the category of the abelian l-groups with strong unit. In this paper, starting from some definitions and results in abelian l-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. |
Clasificación UNESCO | 120105 |
Palabras clave español | Sucesión de Cauchy ; Teoremas de convergencia ; Grupos abelianos ; Algebra completa ; Lógica multivaluada |
Código MathReviews | MR1463107 |
Código Z-Math | Zbl 0939.06010 |
Acceso al artículo completo |