Title: Noncommutative Gröbner Bases and Filtered-Graded Transfer
First published: December 5, 2002
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.
Subjects: Associative rings, Filtered rings, Gröbner bases, Data processing, Algebra, Informatique, Algebre, Nichtkommutative Algebra, Grobner bases, Anneaux filtres, Anneaux associatifs, Ringen (wiskunde), Grobner, Bases de, Grobner-Basis, Computeralgebra, Assoziative Algebra, Algebra, data processing, Mathematics, Algorithms