Separable MV-algebras and lattice-ordered groups

Autores
Marra, Vincenzo; Menni, Matías
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The theory of extensive categories determines in particular the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product of algebras of rational numbers—i.e., of subalgebras of the MV-algebra [0,1]∩Q" role="presentation">. Beyond its intrinsic algebraic interest, this research is motivated by the long-term programme of developing the algebraic geometry of the opposite of the category of MV-algebras, in analogy with the classical case of commutative K-algebras over a field K.
Fil: Marra, Vincenzo. Università degli Studi di Milano; Italia
Fil: Menni, Matías. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Materia
Extensive categories
MV-algebras
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/238351
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Separable MV-algebras and lattice-ordered groupsMarra, VincenzoMenni, MatíasExtensive categoriesMV-algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The theory of extensive categories determines in particular the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product of algebras of rational numbers—i.e., of subalgebras of the MV-algebra [0,1]∩Q" role="presentation">. Beyond its intrinsic algebraic interest, this research is motivated by the long-term programme of developing the algebraic geometry of the opposite of the category of MV-algebras, in analogy with the classical case of commutative K-algebras over a field K.Fil: Marra, Vincenzo. Università degli Studi di Milano; ItaliaFil: Menni, Matías. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaAcademic Press Inc Elsevier Science2024-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/238351Marra, Vincenzo; Menni, Matías; Separable MV-algebras and lattice-ordered groups; Academic Press Inc Elsevier Science; Journal of Algebra; 646; 5-2024; 66-990021-8693CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2024.01.037info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:32:50Zoai:ri.conicet.gov.ar:11336/238351instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 10:32:51.276CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Separable MV-algebras and lattice-ordered groups
title Separable MV-algebras and lattice-ordered groups
spellingShingle Separable MV-algebras and lattice-ordered groups
Marra, Vincenzo
Extensive categories
MV-algebras
title_short Separable MV-algebras and lattice-ordered groups
title_full Separable MV-algebras and lattice-ordered groups
title_fullStr Separable MV-algebras and lattice-ordered groups
title_full_unstemmed Separable MV-algebras and lattice-ordered groups
title_sort Separable MV-algebras and lattice-ordered groups
dc.creator.none.fl_str_mv Marra, Vincenzo
Menni, Matías
author Marra, Vincenzo
author_facet Marra, Vincenzo
Menni, Matías
author_role author
author2 Menni, Matías
author2_role author
dc.subject.none.fl_str_mv Extensive categories
MV-algebras
topic Extensive categories
MV-algebras
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The theory of extensive categories determines in particular the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product of algebras of rational numbers—i.e., of subalgebras of the MV-algebra [0,1]∩Q" role="presentation">. Beyond its intrinsic algebraic interest, this research is motivated by the long-term programme of developing the algebraic geometry of the opposite of the category of MV-algebras, in analogy with the classical case of commutative K-algebras over a field K.
Fil: Marra, Vincenzo. Università degli Studi di Milano; Italia
Fil: Menni, Matías. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
description The theory of extensive categories determines in particular the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product of algebras of rational numbers—i.e., of subalgebras of the MV-algebra [0,1]∩Q" role="presentation">. Beyond its intrinsic algebraic interest, this research is motivated by the long-term programme of developing the algebraic geometry of the opposite of the category of MV-algebras, in analogy with the classical case of commutative K-algebras over a field K.
publishDate 2024
dc.date.none.fl_str_mv 2024-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/238351
Marra, Vincenzo; Menni, Matías; Separable MV-algebras and lattice-ordered groups; Academic Press Inc Elsevier Science; Journal of Algebra; 646; 5-2024; 66-99
0021-8693
CONICET Digital
CONICET
url http://hdl.handle.net/11336/238351
identifier_str_mv Marra, Vincenzo; Menni, Matías; Separable MV-algebras and lattice-ordered groups; Academic Press Inc Elsevier Science; Journal of Algebra; 646; 5-2024; 66-99
0021-8693
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jalgebra.2024.01.037
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.087074

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