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...
- 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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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 |
dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_db06 |
dc.type.content.spa.fl_str_mv |
Text |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TD |
format |
http://purl.org/coar/resource_type/c_db06 |
status_str |
acceptedVersion |
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 |
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application/pdf |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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