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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.

Associative rings --- Grobner bases. --- ALGEBRA --- Filtered rings. --- Gröbner bases --- Algebra --- Filtered rings --- Data processing. --- data processing. --- Data processing --- Grèobner bases --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Associative rings. --- Rings (Algebra). --- Algorithms. --- Associative Rings and Algebras. --- Algorism --- Arithmetic --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Foundations --- Associative rings - Data processing. --- ALGEBRA - data processing. --- Algebra - Data processing