Gröbner bases in ring theory

Huishi Li

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).

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[目次]

  • 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.

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この本の情報

書名 Gröbner bases in ring theory
著作者等 Li, Huishi
出版元 World Scientific
刊行年月 c2012
ページ数 x, 284 p.
大きさ 24 cm
ISBN 9789814365130
NCID BB07168314
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言語 英語
出版国 シンガポール
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