Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups

Autores
Busaniche, Manuela; Cabrer, Leonardo Manuel; Mundici, Daniele
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A unital ℓ-group (G; u) is an abelian group G equipped with a translationinvariant lattice-order and a distinguished element u, called order-unit, whose positive integer multiples eventually dominate each element of G. It is shown that, for direct systems S and T of finitely presented unital ℓ-groups, confluence is a necessary condition for lim S ≅ lim T . (Sufficiency is an easy byproduct of a general result). When (G; u) is finitely generated we equip it with a sequence W (G;u) = (W 0;W 1; : : ) of weighted abstract simplicial complexes, where W t+1 is obtained from W t either by the classical Alexander binary stellar operation, or by deleting a maximal simplex of W t. We show that the map (G; u) → W (G;u) has an inverse. A confluence criterion is given to recognize when two sequences arise from isomorphic unital ℓ-groups.
Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Cabrer, Leonardo Manuel. Universidad Nacional del Centro de la Provincia de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Mundici, Daniele. Università degli Studi di Firenze; Italia
Materia
Abstract Simplicial Complex
Alexander Starring
Confluence
Confluent Direct System
Direct System
Lattice-Ordered Abelian Group
Order-Unit
Rational Polyhedron
Regular Fan
Simplicial Complex
Stellar Subdivision
Weighted Abstract Simplicial Complex
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/67953
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Confluence and combinatorics in finitely generated unital lattice-ordered abelian groupsBusaniche, ManuelaCabrer, Leonardo ManuelMundici, DanieleAbstract Simplicial ComplexAlexander StarringConfluenceConfluent Direct SystemDirect SystemLattice-Ordered Abelian GroupOrder-UnitRational PolyhedronRegular FanSimplicial ComplexStellar SubdivisionWeighted Abstract Simplicial Complexhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A unital ℓ-group (G; u) is an abelian group G equipped with a translationinvariant lattice-order and a distinguished element u, called order-unit, whose positive integer multiples eventually dominate each element of G. It is shown that, for direct systems S and T of finitely presented unital ℓ-groups, confluence is a necessary condition for lim S ≅ lim T . (Sufficiency is an easy byproduct of a general result). When (G; u) is finitely generated we equip it with a sequence W (G;u) = (W 0;W 1; : : ) of weighted abstract simplicial complexes, where W t+1 is obtained from W t either by the classical Alexander binary stellar operation, or by deleting a maximal simplex of W t. We show that the map (G; u) → W (G;u) has an inverse. A confluence criterion is given to recognize when two sequences arise from isomorphic unital ℓ-groups.Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Cabrer, Leonardo Manuel. Universidad Nacional del Centro de la Provincia de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Mundici, Daniele. Università degli Studi di Firenze; ItaliaDe Gruyter2012-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/67953Busaniche, Manuela; Cabrer, Leonardo Manuel; Mundici, Daniele; Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups; De Gruyter; Forum Mathematicum; 24; 2; 3-2012; 253-2710933-7741CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/form.2012.24.issue-2/form.2011.059/form.2011.059.xmlinfo:eu-repo/semantics/altIdentifier/doi/10.1515/form.2011.059info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:04:40Zoai:ri.conicet.gov.ar:11336/67953instacron: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:34982025-10-15 15:04:40.494CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
title Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
spellingShingle Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
Busaniche, Manuela
Abstract Simplicial Complex
Alexander Starring
Confluence
Confluent Direct System
Direct System
Lattice-Ordered Abelian Group
Order-Unit
Rational Polyhedron
Regular Fan
Simplicial Complex
Stellar Subdivision
Weighted Abstract Simplicial Complex
title_short Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
title_full Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
title_fullStr Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
title_full_unstemmed Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
title_sort Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
dc.creator.none.fl_str_mv Busaniche, Manuela
Cabrer, Leonardo Manuel
Mundici, Daniele
author Busaniche, Manuela
author_facet Busaniche, Manuela
Cabrer, Leonardo Manuel
Mundici, Daniele
author_role author
author2 Cabrer, Leonardo Manuel
Mundici, Daniele
author2_role author
author
dc.subject.none.fl_str_mv Abstract Simplicial Complex
Alexander Starring
Confluence
Confluent Direct System
Direct System
Lattice-Ordered Abelian Group
Order-Unit
Rational Polyhedron
Regular Fan
Simplicial Complex
Stellar Subdivision
Weighted Abstract Simplicial Complex
topic Abstract Simplicial Complex
Alexander Starring
Confluence
Confluent Direct System
Direct System
Lattice-Ordered Abelian Group
Order-Unit
Rational Polyhedron
Regular Fan
Simplicial Complex
Stellar Subdivision
Weighted Abstract Simplicial Complex
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A unital ℓ-group (G; u) is an abelian group G equipped with a translationinvariant lattice-order and a distinguished element u, called order-unit, whose positive integer multiples eventually dominate each element of G. It is shown that, for direct systems S and T of finitely presented unital ℓ-groups, confluence is a necessary condition for lim S ≅ lim T . (Sufficiency is an easy byproduct of a general result). When (G; u) is finitely generated we equip it with a sequence W (G;u) = (W 0;W 1; : : ) of weighted abstract simplicial complexes, where W t+1 is obtained from W t either by the classical Alexander binary stellar operation, or by deleting a maximal simplex of W t. We show that the map (G; u) → W (G;u) has an inverse. A confluence criterion is given to recognize when two sequences arise from isomorphic unital ℓ-groups.
Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Cabrer, Leonardo Manuel. Universidad Nacional del Centro de la Provincia de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Mundici, Daniele. Università degli Studi di Firenze; Italia
description A unital ℓ-group (G; u) is an abelian group G equipped with a translationinvariant lattice-order and a distinguished element u, called order-unit, whose positive integer multiples eventually dominate each element of G. It is shown that, for direct systems S and T of finitely presented unital ℓ-groups, confluence is a necessary condition for lim S ≅ lim T . (Sufficiency is an easy byproduct of a general result). When (G; u) is finitely generated we equip it with a sequence W (G;u) = (W 0;W 1; : : ) of weighted abstract simplicial complexes, where W t+1 is obtained from W t either by the classical Alexander binary stellar operation, or by deleting a maximal simplex of W t. We show that the map (G; u) → W (G;u) has an inverse. A confluence criterion is given to recognize when two sequences arise from isomorphic unital ℓ-groups.
publishDate 2012
dc.date.none.fl_str_mv 2012-03
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/11336/67953
Busaniche, Manuela; Cabrer, Leonardo Manuel; Mundici, Daniele; Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups; De Gruyter; Forum Mathematicum; 24; 2; 3-2012; 253-271
0933-7741
CONICET Digital
CONICET
url http://hdl.handle.net/11336/67953
identifier_str_mv Busaniche, Manuela; Cabrer, Leonardo Manuel; Mundici, Daniele; Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups; De Gruyter; Forum Mathematicum; 24; 2; 3-2012; 253-271
0933-7741
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/form.2012.24.issue-2/form.2011.059/form.2011.059.xml
info:eu-repo/semantics/altIdentifier/doi/10.1515/form.2011.059
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
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 13.22299

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