Grobner Bases in Ring Theory - Couverture rigide

Li, Huishi

Couverture rigide

ISBN 10 : 9814365130 ISBN 13 : 9789814365130

Editeur : World Scientific Publishing Co Pte Ltd, 2011

Synopsis

This monograph strives to introduce a solid foundation on the usage of Gröbner 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 Gröbner 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 Gröbner 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 Gröbner 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).

A propos du livre

À propos de la quatrième de couverture

This monograph strives to introduce a solid foundation on the usage of Gr bner 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 Gr bner 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 Gr bner 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 Gr bner 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).

Détails de l'édition

• Éditeur: World Scientific Publishing Co Pte Ltd
• Date d'édition: 2011
• Langue: anglais
• ISBN 10: 9814365130
• ISBN 13: 9789814365130
• Reliure: Relié
• Nombre de pages: 296
• Coordonnées du fabricant: non disponible
• Personne responsable: gpsr@libri.de; gpsr@libri.de; ; Europaallee 1; Bad Hersfeld; 36244; Allemagne