On a Definition of a Variety of Monadic ℓ-Groups

In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is give...

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Detalles Bibliográficos
Autores principales: Castiglioni, José Luis, Lewin, Renato A., Sagastume, Marta Susana
Formato: Articulo
Lenguaje:Inglés
Publicado: 2013
Materias:
Ciencias Exactas
Matemática
Monadic ℓ-groups
Monadic MV algebras
Residuated Lattices
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/139814
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-139814
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Exactas
Matemática
Monadic ℓ-groups
Monadic MV algebras
Residuated Lattices
spellingShingle Ciencias Exactas
Matemática
Monadic ℓ-groups
Monadic MV algebras
Residuated Lattices
Castiglioni, José Luis
Lewin, Renato A.
Sagastume, Marta Susana
On a Definition of a Variety of Monadic ℓ-Groups
topic_facet Ciencias Exactas
Matemática
Monadic ℓ-groups
Monadic MV algebras
Residuated Lattices
description In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor K∙, motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case of MV-algebras and the corresponding category MV∙ of monadic MV-algebras induced by “Kalman’s functor” K∙. Moreover, we extend the construction to ℓ-groups introducing the new category of monadic ℓ-groups together with a functor Γ♯, that is “parallel” to the well known functor Γ between ℓ and MV-algebras.
format Articulo
Articulo
author Castiglioni, José Luis
Lewin, Renato A.
Sagastume, Marta Susana
author_facet Castiglioni, José Luis
Lewin, Renato A.
Sagastume, Marta Susana
author_sort Castiglioni, José Luis
title On a Definition of a Variety of Monadic ℓ-Groups
title_short On a Definition of a Variety of Monadic ℓ-Groups
title_full On a Definition of a Variety of Monadic ℓ-Groups
title_fullStr On a Definition of a Variety of Monadic ℓ-Groups
title_full_unstemmed On a Definition of a Variety of Monadic ℓ-Groups
title_sort on a definition of a variety of monadic ℓ-groups
publishDate 2013
url http://sedici.unlp.edu.ar/handle/10915/139814
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bdutipo_str Repositorios
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