Details:
Title  String Rewriting and Gröbner Bases  A General Approach to Monoid and Group Rings  Author(s)  Klaus Madlener, Birgit Reinert  Type  Technical Report, Misc  Abstract  The concept of algebraic simplification is of great importance for the field of symbolic computation in computer algebra. In this paper we review some fundamental concepts concerning reduction rings in the spirit of Buchberger. The most important properties of reduction rings are presented. 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 noncommutative cases. Several results on the connection of the word problem and the congruence problem are proven. The concepts of saturation and completion are introduced for monoid rings having a finite convergent presentation by a semiThue system. For certain presentations, including free groups and contextfree groups, the existence of finite Gröbner bases for finitely generated right ideals is shown and a procedure to compute them is given.  Length  50 
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 Language  English  Year  1998  Edition  0  Translation 
No  Refereed 
No  Organization 
Universität Kaiserslautern 
