Hello Gap Forum, I would like to know how to create the Free
>Associative Algebra with a one with some small number
>of generators over a field like the rationals and
>then factor out the ideal generated by some few words in the
>generators.

Dear David,
You need a non-commutative Groebner basis package for this. As far as I know
(but maybe I am wrong), there is no such in GAP today. But there exists several
of them outside GAP community. Bergman and Anick are two of them where I
participated myself. Bergman is on LISP/Reduce and works with the homogenious
relations only. Anick is on C and mainly used for calulating Anick resolution
but has a possibility to calulate Groebner basis too. Besides that there are a
lot of term rewriting systems, which can be used too, especially if you works
with the words only.
Your Sincerely
Victor Ufnarovski