Non-commutative reduction rings
Reduction relations are means to express congruences on rings. In the special case of congruences induced by ideals in commutative polynomial rings, the powerful tool of Grabner bases can be characterized by properties of reduction relations associated with ideal bases. Hence, reduction rings can be...
- Autores:
-
Madlener, Klaus
Reinert, Birgit
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1999
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/43726
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/43726
http://bdigital.unal.edu.co/33824/
- Palabra clave:
- Reduction rings
Gröbner bases
non-commutative rings
standard ring constructions
- 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_abf2Madlener, Klausb57a3533-b3f7-49eb-8d43-856d5ddfeece300Reinert, Birgitea2c8d54-7126-4eb4-b806-73afa643b9483002019-06-28T12:22:09Z2019-06-28T12:22:09Z1999https://repositorio.unal.edu.co/handle/unal/43726http://bdigital.unal.edu.co/33824/Reduction relations are means to express congruences on rings. In the special case of congruences induced by ideals in commutative polynomial rings, the powerful tool of Grabner bases can be characterized by properties of reduction relations associated with ideal bases. Hence, reduction rings can be seen as rings with reduction relations associated to subsets of the ring such that every finitely generated ideal has a finite Gröbner basis. This paper gives an axiomatic framework for studying reduction rings including non-commutative rings and explores when and how the property of being a reduction ring is preserved by standard ring constructions such as quotients and sums of reduction rings, as well as extensions to polynomial and monoid rings over reduction rings. Moreover, it is outlined when such reduction rings are effectiveapplication/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/33745Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 33, núm. 1 (1999); 27-49 0034-7426Madlener, Klaus and Reinert, Birgit (1999) Non-commutative reduction rings. Revista Colombiana de Matemáticas; Vol. 33, núm. 1 (1999); 27-49 0034-7426 .Non-commutative reduction ringsArtículo 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/ARTReduction ringsGröbner basesnon-commutative ringsstandard ring constructionsORIGINAL33745-126628-1-PB.pdfapplication/pdf12730731https://repositorio.unal.edu.co/bitstream/unal/43726/1/33745-126628-1-PB.pdfeb0cfff19f103fe01be2ca69028bbdf3MD51THUMBNAIL33745-126628-1-PB.pdf.jpg33745-126628-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg6619https://repositorio.unal.edu.co/bitstream/unal/43726/2/33745-126628-1-PB.pdf.jpg9f81c3a95b64a6f3ea62c70aa2d6534bMD52unal/43726oai:repositorio.unal.edu.co:unal/437262023-02-14 23:05:01.462Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
Non-commutative reduction rings |
| title |
Non-commutative reduction rings |
| spellingShingle |
Non-commutative reduction rings Reduction rings Gröbner bases non-commutative rings standard ring constructions |
| title_short |
Non-commutative reduction rings |
| title_full |
Non-commutative reduction rings |
| title_fullStr |
Non-commutative reduction rings |
| title_full_unstemmed |
Non-commutative reduction rings |
| title_sort |
Non-commutative reduction rings |
| dc.creator.fl_str_mv |
Madlener, Klaus Reinert, Birgit |
| dc.contributor.author.spa.fl_str_mv |
Madlener, Klaus Reinert, Birgit |
| dc.subject.proposal.spa.fl_str_mv |
Reduction rings Gröbner bases non-commutative rings standard ring constructions |
| topic |
Reduction rings Gröbner bases non-commutative rings standard ring constructions |
| description |
Reduction relations are means to express congruences on rings. In the special case of congruences induced by ideals in commutative polynomial rings, the powerful tool of Grabner bases can be characterized by properties of reduction relations associated with ideal bases. Hence, reduction rings can be seen as rings with reduction relations associated to subsets of the ring such that every finitely generated ideal has a finite Gröbner basis. This paper gives an axiomatic framework for studying reduction rings including non-commutative rings and explores when and how the property of being a reduction ring is preserved by standard ring constructions such as quotients and sums of reduction rings, as well as extensions to polynomial and monoid rings over reduction rings. Moreover, it is outlined when such reduction rings are effective |
| publishDate |
1999 |
| dc.date.issued.spa.fl_str_mv |
1999 |
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2019-06-28T12:22:09Z |
| dc.date.available.spa.fl_str_mv |
2019-06-28T12:22:09Z |
| dc.type.spa.fl_str_mv |
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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info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/resource_type/c_6501 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Text |
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http://purl.org/redcol/resource_type/ART |
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http://purl.org/coar/resource_type/c_6501 |
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publishedVersion |
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https://repositorio.unal.edu.co/handle/unal/43726 |
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http://bdigital.unal.edu.co/33824/ |
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https://repositorio.unal.edu.co/handle/unal/43726 http://bdigital.unal.edu.co/33824/ |
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spa |
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spa |
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http://revistas.unal.edu.co/index.php/recolma/article/view/33745 |
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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. 33, núm. 1 (1999); 27-49 0034-7426 |
| dc.relation.references.spa.fl_str_mv |
Madlener, Klaus and Reinert, Birgit (1999) Non-commutative reduction rings. Revista Colombiana de Matemáticas; Vol. 33, núm. 1 (1999); 27-49 0034-7426 . |
| dc.rights.spa.fl_str_mv |
Derechos reservados - Universidad Nacional de Colombia |
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http://purl.org/coar/access_right/c_abf2 |
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Atribución-NoComercial 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc/4.0/ |
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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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Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas |
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Universidad Nacional de Colombia |
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