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  • © 2002

Noncommutative Gröbner Bases and Filtered-Graded Transfer

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1795)

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About this book

This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.

Keywords

  • Filtered ring
  • Gradedring
  • Groebner basis
  • Monomial ordering
  • Solvable polynomial algebra
  • algorithms

Reviews

From the reviews:

MATHEMATICAL REVIEWS

"The monograph covers an important area of research, and the material included may be helpful for researchers and graduate students interested in developing and using Grobner bases in solutions to various mathematical problems. References to many existing computer algebra systems enable the readers to verify methods introduced in this book with the help of computers."

Bibliographic Information

  • Book Title: Noncommutative Gröbner Bases and Filtered-Graded Transfer

  • Authors: Huishi Li

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b84211

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Softcover ISBN: 978-3-540-44196-0Published: 23 October 2002

  • eBook ISBN: 978-3-540-45765-7Published: 19 October 2004

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IX, 202

  • Topics: Associative Rings and Algebras, Algorithms

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions