Gröbner bases in ring theory
- Huishi Li.
- Singapore ; Hackensack, NJ : World Scientific Publishing Co., c2012.
- Physical description
- x, 284 p. : ill ; 24 cm.
Math & Statistics Library
|QA251.3 .L48 2012||Unknown|
- Li, Huishi.
- Includes bibliographical references (p. 271-280) and index.
- The Γ---Leading Homogeneous Algebra AΓ--LH-- 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.
- (source: Nielsen Book Data)9789814365130 20160607
- Publisher's Summary
- 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, this 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).
(source: Nielsen Book Data)9789814365130 20160607
- Publication date
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