This research is concerned with the study of affine rings. The point of view is geometric. Topics to be studied include smoothness, finite global dimension, and integrality. The computer will be used extensively in this project and programs for doing these computations will be developed. This research is in the general area of noncommutative ring theory. It concerns the classification of affine PI-algebras. This is a difficult area but one which is of real interest to the mathematical community. This project involves developing computer software which will be useful to mathematicians working on other projects.
