Author	Li, Huishi. author
Title	Noncommutative Grรถbner Bases and Filtered-Graded Transfer [electronic resource] / by Huishi Li
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2002
Connect to	http://dx.doi.org/10.1007/b84211
Descript	IX, 202 p. online resource

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

Introduction -- Chapter I: Basic Structural Tricks and Examples -- Chapter II: Grรถbner Bases in Associative Algebras -- Chapter III: Grรถbner Bases and Basic Algebraic-Algorithmic Structures -- Chapter IV: Filtered-Graded Transfer of Grรถbner Bases -- Chapter V: GK-dimension of Modules over Quadric Solvable Polynomial Algebras and Elimination of Variables -- Chapter VI: Multiplicity Computation of Modules over Quadric Solvable Polynomial Algebras -- Chapter VII: (partial-)Holonomic Modules and Functions over Quadric Solvable Polynomial Algebras -- Chapter VII: Regularity and Ko-group of Quadric Solvable Polynomial Algebras -- References -- Index

1. Mathematics
2. Associative rings
3. Rings (Algebra)
4. Algorithms
5. Mathematics
6. Associative Rings and Algebras
7. Algorithms