Projective modules and Gröbner bases for skew PBW extensions

Autores
Lezama Serrano, José Oswaldo; Gallego Joya, Claudia Milena
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincare- Birkhoff Witt) extensions. In the present paper we study two aspects of these non-commutative rings: their finitely generated projective modules from a matrix-constructive approach, and the construction of the Gröbner theory for their left ideals and modules. These two topics have interesting applications in functional linear systems and in non-commutative geometry.
Fil: Lezama Serrano, José Oswaldo. Universidad Nacional de Colombia; Colombia
Fil: Gallego Joya, Claudia Milena. Universidad Nacional de Colombia; Colombia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Buchberger&Rsquo;S Algorithm
Hermite Rings
Matrix-Constructive Methods
Non-Commutative GrÖBner Bases
Projective Modules
Skew Pbw Extensions
Stable Rank
Stably Free Modules
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:11336/68736
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/68736
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Projective modules and Gröbner bases for skew PBW extensionsLezama Serrano, José OswaldoGallego Joya, Claudia MilenaBuchberger&Rsquo;S AlgorithmHermite RingsMatrix-Constructive MethodsNon-Commutative GrÖBner BasesProjective ModulesSkew Pbw ExtensionsStable RankStably Free Moduleshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincare- Birkhoff Witt) extensions. In the present paper we study two aspects of these non-commutative rings: their finitely generated projective modules from a matrix-constructive approach, and the construction of the Gröbner theory for their left ideals and modules. These two topics have interesting applications in functional linear systems and in non-commutative geometry.Fil: Lezama Serrano, José Oswaldo. Universidad Nacional de Colombia; ColombiaFil: Gallego Joya, Claudia Milena. Universidad Nacional de Colombia; Colombia. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaPolish Academy of Sciences. Institute of Mathematics2017-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/68736Lezama Serrano, José Oswaldo; Gallego Joya, Claudia Milena; Projective modules and Gröbner bases for skew PBW extensions; Polish Academy of Sciences. Institute of Mathematics; Dissertationes Mathematicae; 521; 1-2017; 1-500012-3862CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4064/dm747-4-2016info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/all/521/0/92028/projective-modules-and-grobner-bases-for-skew-pbw-extensionsinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:02:45Zoai:ri.conicet.gov.ar:11336/68736instacron: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:34982025-10-22 11:02:45.392CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Projective modules and Gröbner bases for skew PBW extensions
title Projective modules and Gröbner bases for skew PBW extensions
spellingShingle Projective modules and Gröbner bases for skew PBW extensions
Lezama Serrano, José Oswaldo
Buchberger&Rsquo;S Algorithm
Hermite Rings
Matrix-Constructive Methods
Non-Commutative GrÖBner Bases
Projective Modules
Skew Pbw Extensions
Stable Rank
Stably Free Modules
title_short Projective modules and Gröbner bases for skew PBW extensions
title_full Projective modules and Gröbner bases for skew PBW extensions
title_fullStr Projective modules and Gröbner bases for skew PBW extensions
title_full_unstemmed Projective modules and Gröbner bases for skew PBW extensions
title_sort Projective modules and Gröbner bases for skew PBW extensions
dc.creator.none.fl_str_mv Lezama Serrano, José Oswaldo
Gallego Joya, Claudia Milena
author Lezama Serrano, José Oswaldo
author_facet Lezama Serrano, José Oswaldo
Gallego Joya, Claudia Milena
author_role author
author2 Gallego Joya, Claudia Milena
author2_role author
dc.subject.none.fl_str_mv Buchberger&Rsquo;S Algorithm
Hermite Rings
Matrix-Constructive Methods
Non-Commutative GrÖBner Bases
Projective Modules
Skew Pbw Extensions
Stable Rank
Stably Free Modules
topic Buchberger&Rsquo;S Algorithm
Hermite Rings
Matrix-Constructive Methods
Non-Commutative GrÖBner Bases
Projective Modules
Skew Pbw Extensions
Stable Rank
Stably Free Modules
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincare- Birkhoff Witt) extensions. In the present paper we study two aspects of these non-commutative rings: their finitely generated projective modules from a matrix-constructive approach, and the construction of the Gröbner theory for their left ideals and modules. These two topics have interesting applications in functional linear systems and in non-commutative geometry.
Fil: Lezama Serrano, José Oswaldo. Universidad Nacional de Colombia; Colombia
Fil: Gallego Joya, Claudia Milena. Universidad Nacional de Colombia; Colombia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Many rings and algebras arising in quantum mechanics, algebraic analysis, and non-commutative algebraic geometry can be interpreted as skew PBW (Poincare- Birkhoff Witt) extensions. In the present paper we study two aspects of these non-commutative rings: their finitely generated projective modules from a matrix-constructive approach, and the construction of the Gröbner theory for their left ideals and modules. These two topics have interesting applications in functional linear systems and in non-commutative geometry.
publishDate 2017
dc.date.none.fl_str_mv 2017-01
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/11336/68736
Lezama Serrano, José Oswaldo; Gallego Joya, Claudia Milena; Projective modules and Gröbner bases for skew PBW extensions; Polish Academy of Sciences. Institute of Mathematics; Dissertationes Mathematicae; 521; 1-2017; 1-50
0012-3862
CONICET Digital
CONICET
url http://hdl.handle.net/11336/68736
identifier_str_mv Lezama Serrano, José Oswaldo; Gallego Joya, Claudia Milena; Projective modules and Gröbner bases for skew PBW extensions; Polish Academy of Sciences. Institute of Mathematics; Dissertationes Mathematicae; 521; 1-2017; 1-50
0012-3862
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4064/dm747-4-2016
info:eu-repo/semantics/altIdentifier/url/https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/all/521/0/92028/projective-modules-and-grobner-bases-for-skew-pbw-extensions
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 Polish Academy of Sciences. Institute of Mathematics
publisher.none.fl_str_mv Polish Academy of Sciences. Institute of Mathematics
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 12.982451

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