Quillen-Suslin Rings
In this paper we introduce the Quillen-Suslin rings and investigate its relation with some other classes of rings as Hermite rings (each stably free module is free), PSF rings (each finitely generated projective module is stably free), PF rings (each finitely generated projective module is free), et...
- Autores:
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2009
- Institución:
- Universidad de Bogotá Jorge Tadeo Lozano
- Repositorio:
- Expeditio: repositorio UTadeo
- Idioma:
- spa
- OAI Identifier:
- oai:expeditiorepositorio.utadeo.edu.co:20.500.12010/28113
- Acceso en línea:
- https://matematicas.unex.es/~extracta/Vol-24-1/24b1Lezama.pdf
http://hdl.handle.net/20.500.12010/28113
http://expeditiorepositorio.utadeo.edu.co
- Palabra clave:
- Quillen-Suslin theorem
Hermite rings
Extended modules and rings
Variedades (Matemáticas)
Teoría de la demostración
Probabilidades
- Rights
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0
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| dc.title.spa.fl_str_mv |
Quillen-Suslin Rings |
| title |
Quillen-Suslin Rings |
| spellingShingle |
Quillen-Suslin Rings Quillen-Suslin theorem Hermite rings Extended modules and rings Variedades (Matemáticas) Teoría de la demostración Probabilidades |
| title_short |
Quillen-Suslin Rings |
| title_full |
Quillen-Suslin Rings |
| title_fullStr |
Quillen-Suslin Rings |
| title_full_unstemmed |
Quillen-Suslin Rings |
| title_sort |
Quillen-Suslin Rings |
| dc.subject.spa.fl_str_mv |
Quillen-Suslin theorem Hermite rings Extended modules and rings |
| topic |
Quillen-Suslin theorem Hermite rings Extended modules and rings Variedades (Matemáticas) Teoría de la demostración Probabilidades |
| dc.subject.lemb.spa.fl_str_mv |
Variedades (Matemáticas) Teoría de la demostración Probabilidades |
| description |
In this paper we introduce the Quillen-Suslin rings and investigate its relation with some other classes of rings as Hermite rings (each stably free module is free), PSF rings (each finitely generated projective module is stably free), PF rings (each finitely generated projective module is free), etc. Quillen-Suslin rings are induced by the famous Serre’s problem formulated by J.P. Serre in 1955 ([30]) and solved independently by Quillen ([28]) and Suslin ([31]) in 1976. The solution is known as the Quillen-Suslin theorem and states that every finitely generated projective module over the polynomial ring K[x1,...,xn] is free, where K is a field. There are algorithmic proofs and some generalizations of this important theorem that we will also study in this paper. In particular, we will consider extended modules and rings, and the Bass-Quillen conjecture. |
| publishDate |
2009 |
| dc.date.created.none.fl_str_mv |
2009 |
| dc.date.accessioned.none.fl_str_mv |
2022-09-15T17:09:49Z |
| dc.date.available.none.fl_str_mv |
2022-09-15T17:09:49Z |
| dc.type.local.spa.fl_str_mv |
Artículo |
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http://purl.org/coar/resource_type/c_6501 |
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http://purl.org/coar/resource_type/c_6501 |
| dc.identifier.issn.spa.fl_str_mv |
0124-2253 |
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https://matematicas.unex.es/~extracta/Vol-24-1/24b1Lezama.pdf |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/20.500.12010/28113 |
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http://expeditiorepositorio.utadeo.edu.co |
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0124-2253 |
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https://matematicas.unex.es/~extracta/Vol-24-1/24b1Lezama.pdf http://hdl.handle.net/20.500.12010/28113 http://expeditiorepositorio.utadeo.edu.co |
| dc.language.iso.spa.fl_str_mv |
spa |
| language |
spa |
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http://purl.org/coar/access_right/c_abf2 |
| dc.rights.license.spa.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0 |
| dc.rights.local.spa.fl_str_mv |
Abierto (Texto Completo) |
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http://creativecommons.org/licenses/by-nc-nd/4.0 Abierto (Texto Completo) http://purl.org/coar/access_right/c_abf2 |
| dc.format.extent.spa.fl_str_mv |
43 páginas |
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application/pdf |
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Colombia |
| dc.publisher.spa.fl_str_mv |
Universidad de Bogotá Jorge Tadeo Lozano |
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instname:Universidad Jorge Tadeo Lozano reponame:Repositorio Institucional UJTL |
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Universidad Jorge Tadeo Lozano |
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Universidad de Bogotá Jorge Tadeo Lozano |
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http://creativecommons.org/licenses/by-nc-nd/4.0EL AUTOR, manifiesta que la obra objeto de la presente autorización es original y la realizó sin violar o usurpar derechos de autor de terceros, por lo tanto la obra es de exclusiva autoría y tiene la titularidad sobre la misma. PARGRAFO: En caso de presentarse cualquier reclamación o acción por parte de un tercero en cuanto a los derechos de autor sobre la obra en cuestión, EL AUTOR, asumirá toda la responsabilidad, y saldrá en defensa de los derechos aquí autorizados; para todos los efectos la universidad actúa como un tercero de buena fe. EL AUTOR, autoriza a LA UNIVERSIDAD DE BOGOTA JORGE TADEO LOZANO, para que en los términos establecidos en la Ley 23 de 1982, Ley 44 de 1993, Decisión andina 351 de 1993, Decreto 460 de 1995 y demás normas generales sobre la materia, utilice y use la obra objeto de la presente autorización. POLITICA DE TRATAMIENTO DE DATOS PERSONALES. Declaro que autorizo previa y de forma informada el tratamiento de mis datos personales por parte de LA UNIVERSIDAD DE BOGOTÁ JORGE TADEO LOZANO para fines académicos y en aplicación de convenios con terceros o servicios conexos con actividades propias de la academia, con estricto cumplimiento de los principios de ley. Para el correcto ejercicio de mi derecho de habeas data cuento con la cuenta de correo protecciondatos@utadeo.edu.co, donde previa identificación podré solicitar la consulta, corrección y supresión de mis datosAbierto (Texto Completo)http://purl.org/coar/access_right/c_abf2Colombia2022-09-15T17:09:49Z2022-09-15T17:09:49Z20090124-2253https://matematicas.unex.es/~extracta/Vol-24-1/24b1Lezama.pdfhttp://hdl.handle.net/20.500.12010/28113http://expeditiorepositorio.utadeo.edu.coIn this paper we introduce the Quillen-Suslin rings and investigate its relation with some other classes of rings as Hermite rings (each stably free module is free), PSF rings (each finitely generated projective module is stably free), PF rings (each finitely generated projective module is free), etc. Quillen-Suslin rings are induced by the famous Serre’s problem formulated by J.P. Serre in 1955 ([30]) and solved independently by Quillen ([28]) and Suslin ([31]) in 1976. The solution is known as the Quillen-Suslin theorem and states that every finitely generated projective module over the polynomial ring K[x1,...,xn] is free, where K is a field. There are algorithmic proofs and some generalizations of this important theorem that we will also study in this paper. In particular, we will consider extended modules and rings, and the Bass-Quillen conjecture.43 páginasapplication/pdfspaUniversidad de Bogotá Jorge Tadeo Lozanoinstname:Universidad Jorge Tadeo Lozanoreponame:Repositorio Institucional UJTLQuillen-Suslin theoremHermite ringsExtended modules and ringsVariedades (Matemáticas)Teoría de la demostraciónProbabilidadesQuillen-Suslin RingsArtículohttp://purl.org/coar/resource_type/c_6501Cegarra, Antonio M.Lezama, O.Cifuentes, V.Fajardo, W.Montaño, J.Pinto, M.Pulido, A.Reyes, M.ORIGINAL24b1Lezama.pdf24b1Lezama.pdfArchivo abierto / Open archiveapplication/pdf330419https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/28113/3/24b1Lezama.pdfac01b06823ece2801009c6ce5a7f8e7bMD53open accessLICENSElicense.txtlicense.txttext/plain; charset=utf-82938https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/28113/2/license.txtbaba314677a6b940f072575a13bb6906MD52open accessTHUMBNAIL24b1Lezama.pdf.jpg24b1Lezama.pdf.jpgIM Thumbnailimage/jpeg8146https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/28113/4/24b1Lezama.pdf.jpgba8963e061a37af19f1ba0338a52d329MD54open access20.500.12010/28113oai:expeditiorepositorio.utadeo.edu.co:20.500.12010/281132024-03-31 03:02:31.838open accessRepositorio Institucional - Universidad Jorge Tadeo Lozanoexpeditiorepositorio@utadeo.edu.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 |