My area of research interest is Ring Theory, a branch of Algebra. A ring is a collection of objects with an addition and a multiplication; the multiplication is not assumed to be commutative, however, and elements need not have multiplicative inverses. (A good example is the collection of all 2 by 2 matrices whose entries are integers.) I’ve tried to write up something about the basics of ring theory.
To be a little more technical, my area of research is non-commutative ring theory, especially Noetherian rings. I have published papers on localization, prime and primitive ideal structure, and some related questions for some standard examples of non-commutative Noetherian rings. Some examples of rings I have been interested in [I haven’t published on all of these types of rings — at least not yet] are group-graded and semigroup-graded rings, enveloping algebras (of Lie algebras, Lie superalgebras, and color Lie algebras), skew polynomial rings, non-commutative regular rings, Hopf algebras, and quantum groups.
Two Ph.D. students have graduated with me as their advisor: Irmgard Redman and Kenneth Price and two more with me as co-advisor: Anthony Van Groningen and Jae Kook Lee.
I am currently working with the following graduate students: Jason Gaddis and Miroslaw Pryszczepko.
The Algebra Research Group at UW-Milwaukee