Buch, Englisch, 296 Seiten, HC gerader Rücken kaschiert, Format (B × H): 157 mm x 235 mm, Gewicht: 582 g
Buch, Englisch, 296 Seiten, HC gerader Rücken kaschiert, Format (B × H): 157 mm x 235 mm, Gewicht: 582 g
ISBN: 978-981-4365-13-0
Verlag: World Scientific
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).
Zielgruppe
Researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry.
Fachgebiete
- Mathematik | Informatik Mathematik Algebra
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Mathematik Interdisziplinär Computeralgebra
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
Weitere Infos & Material
The ?-Leading Homogeneous Algebra A?LH; Gröbner Bases: Conception and Construction; Gröbner Basis Theory Meets PBW Theory; Using ABLH in Terms of Gröbner Bases; Recognizing (Non-)Homogeneous p-Koszulity via ABLH; A Study of Rees Algebra by Gröbner Bases; Looking for More Gröbner Bases.
