Details:
Title  An algorithm for constructing Gröbner and free Schreier bases in free group algebras  Author(s)  Amnon Rosenmann  Type  Article in Journal  Abstract  We present an algorithm for computing Gröbner and free canonical Schreier bases for finitely generated onesided ideals in free group algebras. That is, given a set of n elements of a free group algebra, we construct a canonical Schreier basis of free generators as well as a Gröbner basis for the right ideal generated by the original set. In contrast to Buchberger's algorithm in polynomial rings, at any stage the current number of polynomials does not exceed 2n and their maximal degree is bounded by d 2, where d is the maximal degree of the original polynomials.
A corollary is that the generalised membership problem for free group algebras is solvable.
As a special case we obtain an algorithm similar to the NielsenHall algorithm for constructing free bases for subgroups of free groups.
A generalisation of the notion of a Gröbner basis is given by the definition of algebras satisfying constructive division algorithms.  ISSN  07477171 
URL 
dx.doi.org/10.1006/jsco.1993.1061 
Language  English  Journal  Journal of Symbolic Computation  Volume  16  Number  6  Pages  523549  Publisher  Academic Press, Inc.  Address  Duluth, MN, USA  Year  1993  Translation 
No  Refereed 
Yes 
