Abstract:
The concept of algebraic simplification is of great importance for the field of symbolic computation in computer algebra. In this tutorial we review some fundamental concepts concerning reduction. The techniques for presenting monoids or groups by string rewriting systems are used to define several types of reduction in monoid and group rings. Gröbner bases in this setting arise naturally as generalizations of the corresponding known notions in the commutative and some non-commutative cases. The concepts of saturation and completion are introduced for monoid rings having a finite convergent presentation by a semi-Thue system. They are specialized for cases where the monoid and group presentations provide additional information.

Birgit Reinert
Fachbereich Informatik
Postfach 3049
67653 Kaiserslautern, Germany