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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/67953
Ver los metadatos del registro completo
id |
CONICETDig_04ef60706755789c573a0b2912b99ff0 |
---|---|
oai_identifier_str |
oai:ri.conicet.gov.ar:11336/67953 |
network_acronym_str |
CONICETDig |
repository_id_str |
3498 |
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 Técnicas2025-09-29T10:07:36Zoai: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:34982025-09-29 10:07:36.607CONICET 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 |
_version_ |
1844613938096898048 |
score |
13.070432 |