The dp-rank of abelian groups

An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik–Chervonenkis density. Furthermore, strong abelian groups are characterised to be precisely those abelian groups A such that there...

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Detalles Bibliográficos
Autores: Halevi, Yatir, Palacín Cruz, Daniel
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/98555
Acceso en línea:https://hdl.handle.net/20.500.14352/98555
Access Level:acceso abierto
Palabra clave:Abelian group
One-based
Vc-density
Dp-rank
Lógica simbólica y matemática (Matemáticas)
1102.10 Teoría de Modelos
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spelling The dp-rank of abelian groupsHalevi, YatirPalacín Cruz, DanielAbelian groupOne-basedVc-densityDp-rankLógica simbólica y matemática (Matemáticas)1102.10 Teoría de ModelosAn equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik–Chervonenkis density. Furthermore, strong abelian groups are characterised to be precisely those abelian groups A such that there are only finitely many primes p such that the group A/pA is infinite and for every prime p, there are only finitely many natural numbers n such that (p^n A)[p]/(p^{n + 1} A)[p] is infinite. Finally, it is shown that an infinite stable field of finite dp-rank is algebraically closed.Cambridge University PressUniversidad Complutense de Madrid20192019-01-0120192019-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/98555reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/985552026-06-02T12:44:21Z
dc.title.none.fl_str_mv The dp-rank of abelian groups
title The dp-rank of abelian groups
spellingShingle The dp-rank of abelian groups
Halevi, Yatir
Abelian group
One-based
Vc-density
Dp-rank
Lógica simbólica y matemática (Matemáticas)
1102.10 Teoría de Modelos
title_short The dp-rank of abelian groups
title_full The dp-rank of abelian groups
title_fullStr The dp-rank of abelian groups
title_full_unstemmed The dp-rank of abelian groups
title_sort The dp-rank of abelian groups
dc.creator.none.fl_str_mv Halevi, Yatir
Palacín Cruz, Daniel
author Halevi, Yatir
author_facet Halevi, Yatir
Palacín Cruz, Daniel
author_role author
author2 Palacín Cruz, Daniel
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv Abelian group
One-based
Vc-density
Dp-rank
Lógica simbólica y matemática (Matemáticas)
1102.10 Teoría de Modelos
topic Abelian group
One-based
Vc-density
Dp-rank
Lógica simbólica y matemática (Matemáticas)
1102.10 Teoría de Modelos
description An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik–Chervonenkis density. Furthermore, strong abelian groups are characterised to be precisely those abelian groups A such that there are only finitely many primes p such that the group A/pA is infinite and for every prime p, there are only finitely many natural numbers n such that (p^n A)[p]/(p^{n + 1} A)[p] is infinite. Finally, it is shown that an infinite stable field of finite dp-rank is algebraically closed.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01
2019
2019-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/98555
url https://hdl.handle.net/20.500.14352/98555
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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