The Word Problem and Relations in Rings (2003)
progress report  

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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 T-ideal. I showed that this algorithm could be used to provide computational proofs of some theorems in the non-commutative ring theory literature. This article is a progress report on that work.