Noncommutative Gröbner Bases and Filtered-Graded Transfer
Edition: 1 edition
Publisher: Springer
Published: December 5, 2002
Language: eng
Format: Paperback
Number of pages: 197
ISBN-13: 9783540441960
Subjects: Groups & group theory; Rings; Grobner bases; Algebra; Mathematics; Programming - Algorithms; Science/Mathematics; Group Theory; Algebra - General; General; Filtered ring; Gradedring; Groebner basis; Mathematics / Algebra / General; Monomial ordering; Solvable polynomial algebra; Associative rings; Data processing; Filtered rings; Grèobner bases
First sentence: We assume that the reader is familiar with basic ring theory and module theory.
Description: 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.
Notes: Lecture Notes in Mathematics