Extended modules over skew PBW extensions

In the book “Serre’s problem on projective modules” [42], Tsit Yuen Lam defines the class E of extended rings; these rings satisfy the extended version of the Quillen-Suslin theorem. In this thesis we investigate extended modules and rings for skew P BW extensions from a matrix-constructive approach...

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Autores:
Fajardo Cardenas, William Alfredo
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2019
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/69139
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/69139
http://bdigital.unal.edu.co/70655/
Palabra clave:
51 Matemáticas / Mathematics
Extended modules
Extended rings
Skew P BW extensions
Bass-Quillen conjecture
Quillen-Suslin theorem
Matrix-constructive
algorithmic proofs
Gröbner basis
Skew P BW extensions
Módulos extendidos
Anillos extendidos
Extensiones P BW torcidas
Conjetura de Bass-Quillen
Teorema de Quillen-Suslin
Aproximación matricial constructiva
Pruebas algorítmicas
Bases de Gröbner
Extensiones P BW torcidas
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Lezama Serrano, José OswaldoFajardo Cardenas, William Alfredob1992d24-18fa-4e1e-8078-f7cd9c57ff273002019-07-03T10:16:55Z2019-07-03T10:16:55Z2019-01-23https://repositorio.unal.edu.co/handle/unal/69139http://bdigital.unal.edu.co/70655/In the book “Serre’s problem on projective modules” [42], Tsit Yuen Lam defines the class E of extended rings; these rings satisfy the extended version of the Quillen-Suslin theorem. In this thesis we investigate extended modules and rings for skew P BW extensions from a matrix-constructive approach. We determine conditions on the parameters that define a skew extension A = σ(R)hx1, . . . , xni in order to A be projective-free (PF), or more generally, extended (E). Under such particular conditions we prove Vaserstein’s, Quillen’s patching, Horrocks’ and Quillen-Suslin’s theorems for this type of non-commutative rings of polynomial type. Complementary, but as a very important part of the thesis, a computational package has been developed not only for the computations involved in the matrix-constructive proofs related to the PF and E properties, but also for many homological applications of the Gr¨obner theory of skew P BW extensions developed recently in many papers.En el libro “Serre’s problem on projective modules” [42], Tsit Yuen Lam definió las clases E de anillos extendidos; estas clases de anillos satisfacen la versión extendida del teorema de Quillen-Suslin. En esta tesis investigamos módulos y anillos extendidos para extensiones P BW torcidas desde una aproximación matricial. Determinamos condiciones sobre los parámetros que definen una extensi´on torcida A = σ(R)hx1, . . . , xni para que A sea proyectivo-libre (PF), o más general, extendida (E). Bajo tales condiciones particulares nosotros probamos los teoremas de Vaserstein, patching de Quillen, Horrocks y QuillenSuslin para este tipo de anillos polinomiales no conmutativos. Como complemento, pero como una muy importante parte de la tesis, algunos paquetes han sido desarrollados no solo para cálculos que envueltos en la prueba matricial constructiva relacionada a las propiedades PF y E, sino también para algunas aplicaciones homológicas de la teoría de bases de Gröbner de extensiones P BW torcidas desarrolladas recientemente en muchos trabajosDoctoradoapplication/pdfspaUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Matemáticas MatemáticasMatemáticasFajardo Cardenas, William Alfredo (2019) Extended modules over skew PBW extensions. Doctorado thesis, Universidad Nacional de Colombia - Sede Bogotá.51 Matemáticas / MathematicsExtended modulesExtended ringsSkew P BW extensionsBass-Quillen conjectureQuillen-Suslin theoremMatrix-constructivealgorithmic proofsGröbner basisSkew P BW extensionsMódulos extendidosAnillos extendidosExtensiones P BW torcidasConjetura de Bass-QuillenTeorema de Quillen-SuslinAproximación matricial constructivaPruebas algorítmicasBases de GröbnerExtensiones P BW torcidasExtended modules over skew PBW extensionsTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDORIGINALExtended_Modules_Over_Skew_PBW_Extensions.pdfapplication/pdf854537https://repositorio.unal.edu.co/bitstream/unal/69139/1/Extended_Modules_Over_Skew_PBW_Extensions.pdff342fbe5a78f92d82e476011bcda5112MD51THUMBNAILExtended_Modules_Over_Skew_PBW_Extensions.pdf.jpgExtended_Modules_Over_Skew_PBW_Extensions.pdf.jpgGenerated Thumbnailimage/jpeg3975https://repositorio.unal.edu.co/bitstream/unal/69139/2/Extended_Modules_Over_Skew_PBW_Extensions.pdf.jpg91b0c46fa53ddec7f7ea7945263169c5MD52unal/69139oai:repositorio.unal.edu.co:unal/691392024-05-30 23:13:26.709Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Extended modules over skew PBW extensions
title Extended modules over skew PBW extensions
spellingShingle Extended modules over skew PBW extensions
51 Matemáticas / Mathematics
Extended modules
Extended rings
Skew P BW extensions
Bass-Quillen conjecture
Quillen-Suslin theorem
Matrix-constructive
algorithmic proofs
Gröbner basis
Skew P BW extensions
Módulos extendidos
Anillos extendidos
Extensiones P BW torcidas
Conjetura de Bass-Quillen
Teorema de Quillen-Suslin
Aproximación matricial constructiva
Pruebas algorítmicas
Bases de Gröbner
Extensiones P BW torcidas
title_short Extended modules over skew PBW extensions
title_full Extended modules over skew PBW extensions
title_fullStr Extended modules over skew PBW extensions
title_full_unstemmed Extended modules over skew PBW extensions
title_sort Extended modules over skew PBW extensions
dc.creator.fl_str_mv Fajardo Cardenas, William Alfredo
dc.contributor.author.spa.fl_str_mv Fajardo Cardenas, William Alfredo
dc.contributor.spa.fl_str_mv Lezama Serrano, José Oswaldo
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
topic 51 Matemáticas / Mathematics
Extended modules
Extended rings
Skew P BW extensions
Bass-Quillen conjecture
Quillen-Suslin theorem
Matrix-constructive
algorithmic proofs
Gröbner basis
Skew P BW extensions
Módulos extendidos
Anillos extendidos
Extensiones P BW torcidas
Conjetura de Bass-Quillen
Teorema de Quillen-Suslin
Aproximación matricial constructiva
Pruebas algorítmicas
Bases de Gröbner
Extensiones P BW torcidas
dc.subject.proposal.spa.fl_str_mv Extended modules
Extended rings
Skew P BW extensions
Bass-Quillen conjecture
Quillen-Suslin theorem
Matrix-constructive
algorithmic proofs
Gröbner basis
Skew P BW extensions
Módulos extendidos
Anillos extendidos
Extensiones P BW torcidas
Conjetura de Bass-Quillen
Teorema de Quillen-Suslin
Aproximación matricial constructiva
Pruebas algorítmicas
Bases de Gröbner
Extensiones P BW torcidas
description In the book “Serre’s problem on projective modules” [42], Tsit Yuen Lam defines the class E of extended rings; these rings satisfy the extended version of the Quillen-Suslin theorem. In this thesis we investigate extended modules and rings for skew P BW extensions from a matrix-constructive approach. We determine conditions on the parameters that define a skew extension A = σ(R)hx1, . . . , xni in order to A be projective-free (PF), or more generally, extended (E). Under such particular conditions we prove Vaserstein’s, Quillen’s patching, Horrocks’ and Quillen-Suslin’s theorems for this type of non-commutative rings of polynomial type. Complementary, but as a very important part of the thesis, a computational package has been developed not only for the computations involved in the matrix-constructive proofs related to the PF and E properties, but also for many homological applications of the Gr¨obner theory of skew P BW extensions developed recently in many papers.
publishDate 2019
dc.date.accessioned.spa.fl_str_mv 2019-07-03T10:16:55Z
dc.date.available.spa.fl_str_mv 2019-07-03T10:16:55Z
dc.date.issued.spa.fl_str_mv 2019-01-23
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
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dc.type.content.spa.fl_str_mv Text
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format http://purl.org/coar/resource_type/c_db06
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dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/69139
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/70655/
url https://repositorio.unal.edu.co/handle/unal/69139
http://bdigital.unal.edu.co/70655/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Matemáticas Matemáticas
Matemáticas
dc.relation.references.spa.fl_str_mv Fajardo Cardenas, William Alfredo (2019) Extended modules over skew PBW extensions. Doctorado thesis, Universidad Nacional de Colombia - Sede Bogotá.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
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