On the connectedness of the spectrum of forcing algebras
We study the connectedness property of the spectrum of forcing algebras over a noetherian ring. In particular we present for an integral base ring a geometric criterion for connectedness in terms of horizontal and vertical components of the forcing algebra. This criterion allows further simplificati...
- Autores:
-
Brenner, Holger
Gómez-Ramírez, Danny de Jesús
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2014
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/49345
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/49345
http://bdigital.unal.edu.co/42802/
- Palabra clave:
- Álgebra de forzado
conexidad
clausura entera
13B22
14A15
14R25
54D05
Forcing algebra
Connectedness
Integral closure
- 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_abf2Brenner, Holgera744853d-2cc1-492d-88c2-ea84ba4456ce300Gómez-Ramírez, Danny de Jesúsce884cc0-16c9-4996-8865-f8b85c5759143002019-06-29T08:36:50Z2019-06-29T08:36:50Z2014-06-25https://repositorio.unal.edu.co/handle/unal/49345http://bdigital.unal.edu.co/42802/We study the connectedness property of the spectrum of forcing algebras over a noetherian ring. In particular we present for an integral base ring a geometric criterion for connectedness in terms of horizontal and vertical components of the forcing algebra. This criterion allows further simplifications when the base ring is local, or one--dimensional, or factorial. Besides, we discuss whether the connectedness of forcing algebras is a local property. Finally, we present a characterization of the integral closure of an ideal by means of the universal connectedness of the corresponding forcing morphism.Estudiamos la conexidad del espectro de álgebras de forzado sobre anillo noetherianos. En particular, presentamos un criterio de conexidad cuando el anillo base es un dominio en términos de las componentes verticales y horizontales del álgebra de forzado. Este criterio nos permite obtener simplificaciones en el caso en el que el anillo base es local, o 1--dimensional o un dominio de factorización única. Además, discutimos sobre si la conexidad de las álgebras de forzado es una propiedad local. Finalmente, presentamos una caracterización de pertenencia a la clausura entera de un ideal en términos de la conexidad universal del correspondiente morfismo de forzado.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/45192Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 48, núm. 1 (2014); 1-19 2357-4100 0034-7426Brenner, Holger and Gómez-Ramírez, Danny de Jesús (2014) On the connectedness of the spectrum of forcing algebras. Revista Colombiana de Matemáticas; Vol. 48, núm. 1 (2014); 1-19 2357-4100 0034-7426 .On the connectedness of the spectrum of forcing algebrasArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTÁlgebra de forzadoconexidadclausura entera13B2214A1514R2554D05Forcing algebraConnectednessIntegral closureORIGINAL45192-216969-1-PB.htmltext/html5131https://repositorio.unal.edu.co/bitstream/unal/49345/1/45192-216969-1-PB.htmlb1ba5866b783805263ffe0430f9a42d6MD5145192-216955-1-SM.pdfapplication/pdf565968https://repositorio.unal.edu.co/bitstream/unal/49345/2/45192-216955-1-SM.pdf7bee59c9f2ec906d6b8137d32bbf66d7MD52THUMBNAIL45192-216955-1-SM.pdf.jpg45192-216955-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg5450https://repositorio.unal.edu.co/bitstream/unal/49345/3/45192-216955-1-SM.pdf.jpg24e2348a0faa1f848ef77c59f2c1bc47MD53unal/49345oai:repositorio.unal.edu.co:unal/493452022-12-14 23:04:00.236Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
On the connectedness of the spectrum of forcing algebras |
| title |
On the connectedness of the spectrum of forcing algebras |
| spellingShingle |
On the connectedness of the spectrum of forcing algebras Álgebra de forzado conexidad clausura entera 13B22 14A15 14R25 54D05 Forcing algebra Connectedness Integral closure |
| title_short |
On the connectedness of the spectrum of forcing algebras |
| title_full |
On the connectedness of the spectrum of forcing algebras |
| title_fullStr |
On the connectedness of the spectrum of forcing algebras |
| title_full_unstemmed |
On the connectedness of the spectrum of forcing algebras |
| title_sort |
On the connectedness of the spectrum of forcing algebras |
| dc.creator.fl_str_mv |
Brenner, Holger Gómez-Ramírez, Danny de Jesús |
| dc.contributor.author.spa.fl_str_mv |
Brenner, Holger Gómez-Ramírez, Danny de Jesús |
| dc.subject.proposal.spa.fl_str_mv |
Álgebra de forzado conexidad clausura entera 13B22 14A15 14R25 54D05 Forcing algebra Connectedness Integral closure |
| topic |
Álgebra de forzado conexidad clausura entera 13B22 14A15 14R25 54D05 Forcing algebra Connectedness Integral closure |
| description |
We study the connectedness property of the spectrum of forcing algebras over a noetherian ring. In particular we present for an integral base ring a geometric criterion for connectedness in terms of horizontal and vertical components of the forcing algebra. This criterion allows further simplifications when the base ring is local, or one--dimensional, or factorial. Besides, we discuss whether the connectedness of forcing algebras is a local property. Finally, we present a characterization of the integral closure of an ideal by means of the universal connectedness of the corresponding forcing morphism. |
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2014 |
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2014-06-25 |
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2019-06-29T08:36:50Z |
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2019-06-29T08:36:50Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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https://repositorio.unal.edu.co/handle/unal/49345 |
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http://bdigital.unal.edu.co/42802/ |
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https://repositorio.unal.edu.co/handle/unal/49345 http://bdigital.unal.edu.co/42802/ |
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spa |
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spa |
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http://revistas.unal.edu.co/index.php/recolma/article/view/45192 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas |
| dc.relation.ispartofseries.none.fl_str_mv |
Revista Colombiana de Matemáticas; Vol. 48, núm. 1 (2014); 1-19 2357-4100 0034-7426 |
| dc.relation.references.spa.fl_str_mv |
Brenner, Holger and Gómez-Ramírez, Danny de Jesús (2014) On the connectedness of the spectrum of forcing algebras. Revista Colombiana de Matemáticas; Vol. 48, núm. 1 (2014); 1-19 2357-4100 0034-7426 . |
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Derechos reservados - Universidad Nacional de Colombia |
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Atribución-NoComercial 4.0 Internacional |
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info:eu-repo/semantics/openAccess |
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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 |
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