Noncommutative Gröbner Bases and Filtered-Graded Transfer

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