

The Word Problem and Relations in Rings (2003)
progress report
view/download (pdf)
The
Word Problem is to develop an algorithm which, for an arbitrary set
of generators G and an arbitrary set of relations R, will determine if two
words in G are equivalent or not with respect to the relations in R. The
Word Problem is known to be undecideable. It is equivalent to the ideal membership
problem in ring theory (provide an algorithm to decide if an element of a
ring is in a given ideal). In my article on commutativity theorems
I developed an algorithm with applications to membership in a Tideal. I
showed that this algorithm could be used to provide computational proofs
of some theorems in the noncommutative ring theory literature. This article
is a progress report on that work.

