Allen D. Bell

NOTE: This is an outdated version of my web site.  It only contains some parts of the old site and contains pages that were last updated anywhere from 2008 to 2012.

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