Grobner Bases In Ring Theory
Seiten
2011
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-4365-13-0 (ISBN)
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-4365-13-0 (ISBN)
A monograph that strives to introduce a foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It reveals the intrinsic structural properties of Grobner bases. It presents a constructive PBW theory in a quite extensive context.
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).
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).
The Γ-Leading Homogeneous Algebra AΓLH; Grobner Bases: Conception and Construction; Grobner Basis Theory Meets PBW Theory; Using ABLH in Terms of Grobner Bases; Recognizing (Non-)Homogeneous p-Koszulity via ABLH; A Study of Rees Algebra by Grobner Bases; Looking for More Grobner Bases.
Verlagsort | Singapore |
---|---|
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
ISBN-10 | 981-4365-13-0 / 9814365130 |
ISBN-13 | 978-981-4365-13-0 / 9789814365130 |
Zustand | Neuware |
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