### Research Focus

Algebra, algorithms

First I worked in the area of Hopf algebras and wrote Hopf Algebras, which came to be the standard reference book on the subject. H. Allen and I used Hopf algebras to prove a 25-year-old conjecture of Jacobson. Over the ensuing years until about the mid eighties, I worked and published in the areas of commutative algebra and algebraic geometry, real-algebraic geometry, homological algebra, algebraic groups, purely inseparable field extensions and general positive characteristic phenomena, simple algebras and generalizations of the Brauer group, and differential algebra. Since the mid eighties I have primarily worked in the area of computer algebra, especially computational commutative algebra. This has produced both theoretical and applied results with applications beyond mathematics, such as to error control codes and resulted in my position as Director of the Army Center of Excellence for computer algebra.

### Publications

- Groups of simple algebras, Institut des Hautes Etudes Scientifiques 44 (1975), 79–189.
- A new invariant for the complex numbers over the real numbers (with D. Haile and R. Larson), American Journal of Mathematics 105 (1983), 689–814.
- Gröbner bases for linear recursion relations on m-D arrays and applications to decoding (with I. Rubio and C. Heegard), Proc. IEEE Int'l Symp. on Information Theory, June 29–July 4, 1997, Ulm, Germany.
- Remarks on automatic algorithm stabilization (with K. Shirayanagi), invited contribution to (fourth) IMACS Conf. on Appl. of Computer Algebra (1998).
- Ideal and subalgebra coefficients (with L. Robbiano), Proceedings of the AMS (1998), to appear.