Grobner bases in ring theory:
This monograph strives to introduce a solid foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Grobner bases, presents a constructive PBW theory in a qu...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2012
|
| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | This monograph strives to introduce a solid foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Grobner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Grobner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non-)homogeneous p-Koszulity, PBW-deformation, and regular central extension. With a self-contained and constructive Grobner basis theory for algebras with a skew multiplicative K-basis, numerous illuminating examples are constructed in the book for illustrating and extending the topics studied. Moreover, perspectives of further study on the topics are prompted at appropriate points. This book can be of considerable interest to researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry; especially for those working on the structure theory of rings, algebras and their modules (representations) |
| Beschreibung: | x, 284 p |
| ISBN: | 9789814365147 |
Internformat
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| 520 | |a This monograph strives to introduce a solid foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Grobner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Grobner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non-)homogeneous p-Koszulity, PBW-deformation, and regular central extension. With a self-contained and constructive Grobner basis theory for algebras with a skew multiplicative K-basis, numerous illuminating examples are constructed in the book for illustrating and extending the topics studied. Moreover, perspectives of further study on the topics are prompted at appropriate points. This book can be of considerable interest to researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry; especially for those working on the structure theory of rings, algebras and their modules (representations) | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Li, Huishi |
| author_facet | Li, Huishi |
| author_role | aut |
| author_sort | Li, Huishi |
| author_variant | h l hl |
| building | Verbundindex |
| bvnumber | BV044638680 |
| classification_rvk | SK 230 |
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| ctrlnum | (ZDB-124-WOP)00002532 (OCoLC)1005228903 (DE-599)BVBBV044638680 |
| dewey-full | 512.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.4 |
| dewey-search | 512.4 |
| dewey-sort | 3512.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV044638680 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:54Z |
| institution | BVB |
| isbn | 9789814365147 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030036654 |
| oclc_num | 1005228903 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | x, 284 p |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| spelling | Li, Huishi Verfasser aut Grobner bases in ring theory Huishi Li Singapore World Scientific Pub. Co. c2012 x, 284 p txt rdacontent c rdamedia cr rdacarrier This monograph strives to introduce a solid foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Grobner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Grobner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non-)homogeneous p-Koszulity, PBW-deformation, and regular central extension. With a self-contained and constructive Grobner basis theory for algebras with a skew multiplicative K-basis, numerous illuminating examples are constructed in the book for illustrating and extending the topics studied. Moreover, perspectives of further study on the topics are prompted at appropriate points. This book can be of considerable interest to researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry; especially for those working on the structure theory of rings, algebras and their modules (representations) Grobner bases Rings (Algebra) Computeralgebra (DE-588)4010449-7 gnd rswk-swf Gröbner-Basis (DE-588)4276378-2 gnd rswk-swf Ringtheorie (DE-588)4126571-3 gnd rswk-swf Ringtheorie (DE-588)4126571-3 s Gröbner-Basis (DE-588)4276378-2 s Computeralgebra (DE-588)4010449-7 s DE-604 Erscheint auch als Druck-Ausgabe 9789814365130 Erscheint auch als Druck-Ausgabe 9814365130 http://www.worldscientific.com/worldscibooks/10.1142/8223#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Li, Huishi Grobner bases in ring theory Grobner bases Rings (Algebra) Computeralgebra (DE-588)4010449-7 gnd Gröbner-Basis (DE-588)4276378-2 gnd Ringtheorie (DE-588)4126571-3 gnd |
| subject_GND | (DE-588)4010449-7 (DE-588)4276378-2 (DE-588)4126571-3 |
| title | Grobner bases in ring theory |
| title_auth | Grobner bases in ring theory |
| title_exact_search | Grobner bases in ring theory |
| title_full | Grobner bases in ring theory Huishi Li |
| title_fullStr | Grobner bases in ring theory Huishi Li |
| title_full_unstemmed | Grobner bases in ring theory Huishi Li |
| title_short | Grobner bases in ring theory |
| title_sort | grobner bases in ring theory |
| topic | Grobner bases Rings (Algebra) Computeralgebra (DE-588)4010449-7 gnd Gröbner-Basis (DE-588)4276378-2 gnd Ringtheorie (DE-588)4126571-3 gnd |
| topic_facet | Grobner bases Rings (Algebra) Computeralgebra Gröbner-Basis Ringtheorie |
| url | http://www.worldscientific.com/worldscibooks/10.1142/8223#t=toc |
| work_keys_str_mv | AT lihuishi grobnerbasesinringtheory |