# Convergence in MV-algebras.

• Volume: 4, Issue: 1, page 41-52
• ISSN: 1134-5632

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## Abstract

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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.

## How to cite

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Georgescu, George, Liguori, Fortuna, and Martini, Giulia. "Convergence in MV-algebras.." Mathware and Soft Computing 4.1 (1997): 41-52. <http://eudml.org/doc/39099>.

@article{Georgescu1997,
abstract = {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.},
author = {Georgescu, George, Liguori, Fortuna, Martini, Giulia},
journal = {Mathware and Soft Computing},
keywords = {Sucesión de Cauchy; Teoremas de convergencia; Grupos abelianos; Algebra completa; Lógica multivaluada; convergent sequences; Cauchy sequences; MV-algebra; Cauchy completion; complete MV-algebra; atomic},
language = {eng},
number = {1},
pages = {41-52},
title = {Convergence in MV-algebras.},
url = {http://eudml.org/doc/39099},
volume = {4},
year = {1997},
}

TY - JOUR
AU - Georgescu, George
AU - Liguori, Fortuna
AU - Martini, Giulia
TI - Convergence in MV-algebras.
JO - Mathware and Soft Computing
PY - 1997
VL - 4
IS - 1
SP - 41
EP - 52
AB - 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.
LA - eng
KW - Sucesión de Cauchy; Teoremas de convergencia; Grupos abelianos; Algebra completa; Lógica multivaluada; convergent sequences; Cauchy sequences; MV-algebra; Cauchy completion; complete MV-algebra; atomic
UR - http://eudml.org/doc/39099
ER -

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