A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type
In this paper we present a survey of some algebraic characterizations of Hilbert’s Nullstellensatz for non-commutative rings of polynomial type. Using several results established in the literature, we obtain a version of this theorem for the skew Poincaré-Birkhoff-Witt extensions. Once this is done,...
- Autores:
-
Reyes, Armando
Hernández-Mogollón, Jason
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- eng
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/17662
- Acceso en línea:
- http://hdl.handle.net/10784/17662
- Palabra clave:
- Hilbert’s Nullstellensatz
Skew PBW extension
Jacobson ring
Generic flatness
Teorema de ceros de Hilbert
Extensión PBW torcida
Anillo de Jacobson
Plenitud genérica
- Rights
- License
- Copyright © 2020 Armando Reyes, Jason Hernández-Mogollón
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Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees2020-06-192020-09-04T16:41:31Z2020-06-192020-09-04T16:41:31Z1794-9165http://hdl.handle.net/10784/17662In this paper we present a survey of some algebraic characterizations of Hilbert’s Nullstellensatz for non-commutative rings of polynomial type. Using several results established in the literature, we obtain a version of this theorem for the skew Poincaré-Birkhoff-Witt extensions. Once this is done, we illustrate the Nullstellensatz with examples appearing in noncommutative ring theory and non-commutative algebraic geometry.En este artículo presentamos un estudio sobre algunas caracterizaciones algebraicas del teorema de Nullstellensatz de Hilbert para anillos no conmutativos de tipo polinomial. Utilizando varios resultados establecidos en la literatura, obtuvimos una versión de este teorema para las extensiones de Poincaré-Birkhoff-Witt. Una vez hecho esto, ilustramos el Nullstellensatz con ejemplos que aparecen en la teoría de los anillos no conmutativa y en la geometría algebraica no conmutativa.application/pdfengUniversidad EAFIThttps://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6023https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6023Copyright © 2020 Armando Reyes, Jason Hernández-MogollónAcceso abiertohttp://purl.org/coar/access_right/c_abf2Ingeniería y Ciencia, Vol. 16, Núm. 31 (2020)A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial TypeUn estudio sobre algunas caracterizaciones algebraicas del teorema de ceros de Hilbert para anillos no conmutativos de tipo polinomialarticleinfo:eu-repo/semantics/articlepublishedVersioninfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Hilbert’s NullstellensatzSkew PBW extensionJacobson ringGeneric flatnessTeorema de ceros de HilbertExtensión PBW torcidaAnillo de JacobsonPlenitud genéricaReyes, ArmandoHernández-Mogollón, JasonUniversidad Nacional de ColombiaIngeniería y Ciencia16312752THUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/1443760f-15bb-4463-b155-ab2c1f357968/downloadda9b21a5c7e00c7f1127cef8e97035e0MD51ORIGINAL6023-Article Text-21866-1-10-20200620.pdf6023-Article Text-21866-1-10-20200620.pdfTexto completo PDFapplication/pdf625673https://repository.eafit.edu.co/bitstreams/48f65ed0-3636-46a4-b8f4-32aa5e07b7cb/downloadc3440e6c9bd720649508bab7468d478bMD52articulo - copia (2).htmlarticulo - copia (2).htmlTexto completo HTMLtext/html375https://repository.eafit.edu.co/bitstreams/0164ca83-5fd7-4f41-ab02-3a6d07dc092c/download5ff6a957eb9ee9fbaa0cf43d74a42aeaMD5310784/17662oai:repository.eafit.edu.co:10784/176622020-09-21 08:49:21.208open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co |
| dc.title.eng.fl_str_mv |
A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type |
| dc.title.spa.fl_str_mv |
Un estudio sobre algunas caracterizaciones algebraicas del teorema de ceros de Hilbert para anillos no conmutativos de tipo polinomial |
| title |
A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type |
| spellingShingle |
A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type Hilbert’s Nullstellensatz Skew PBW extension Jacobson ring Generic flatness Teorema de ceros de Hilbert Extensión PBW torcida Anillo de Jacobson Plenitud genérica |
| title_short |
A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type |
| title_full |
A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type |
| title_fullStr |
A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type |
| title_full_unstemmed |
A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type |
| title_sort |
A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type |
| dc.creator.fl_str_mv |
Reyes, Armando Hernández-Mogollón, Jason |
| dc.contributor.author.spa.fl_str_mv |
Reyes, Armando Hernández-Mogollón, Jason |
| dc.contributor.affiliation.spa.fl_str_mv |
Universidad Nacional de Colombia |
| dc.subject.keyword.eng.fl_str_mv |
Hilbert’s Nullstellensatz Skew PBW extension Jacobson ring Generic flatness |
| topic |
Hilbert’s Nullstellensatz Skew PBW extension Jacobson ring Generic flatness Teorema de ceros de Hilbert Extensión PBW torcida Anillo de Jacobson Plenitud genérica |
| dc.subject.keyword.spa.fl_str_mv |
Teorema de ceros de Hilbert Extensión PBW torcida Anillo de Jacobson Plenitud genérica |
| description |
In this paper we present a survey of some algebraic characterizations of Hilbert’s Nullstellensatz for non-commutative rings of polynomial type. Using several results established in the literature, we obtain a version of this theorem for the skew Poincaré-Birkhoff-Witt extensions. Once this is done, we illustrate the Nullstellensatz with examples appearing in noncommutative ring theory and non-commutative algebraic geometry. |
| publishDate |
2020 |
| dc.date.available.none.fl_str_mv |
2020-09-04T16:41:31Z |
| dc.date.issued.none.fl_str_mv |
2020-06-19 |
| dc.date.accessioned.none.fl_str_mv |
2020-09-04T16:41:31Z |
| dc.date.none.fl_str_mv |
2020-06-19 |
| dc.type.eng.fl_str_mv |
article info:eu-repo/semantics/article publishedVersion info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
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Artículo |
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publishedVersion |
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1794-9165 |
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http://hdl.handle.net/10784/17662 |
| identifier_str_mv |
1794-9165 |
| url |
http://hdl.handle.net/10784/17662 |
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eng |
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eng |
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https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6023 |
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https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6023 |
| dc.rights.eng.fl_str_mv |
Copyright © 2020 Armando Reyes, Jason Hernández-Mogollón |
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http://purl.org/coar/access_right/c_abf2 |
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Acceso abierto |
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Copyright © 2020 Armando Reyes, Jason Hernández-Mogollón Acceso abierto http://purl.org/coar/access_right/c_abf2 |
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application/pdf |
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Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees |
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Universidad EAFIT |
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Ingeniería y Ciencia, Vol. 16, Núm. 31 (2020) |
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Universidad EAFIT |
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