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.
I'd like to point you to a Ring Theory Web page, but I'm not
aware of one. I can point you to a
list of some ring theorists' home pages.
I can also point you to an
archive of quantum groups preprints.
Note: these
preprints are compressed by gzip. Your browser is
supposed to automatically uncompress them when you download files,
but this doesn't work for a number of browsers -- look here for
more information.
If your browser doesn't do the work automatically, you have
to (a) name the downloaded file filename.gz then
(b) run the command gunzip filename in order to
uncompress it.
(If it's a special type of file, use the proper extension,
e.g., filename.ps.gz for Postscript files.)
Two Ph.D. students have graduated with me as their advisor:
Irmgard Redman and Kenneth Price.
I am currently working with the following graduate students:
Miroslaw Pryszczepko and Anthony Van Groningen.
You can view a list of my publications, with links to abstracts.
You can obtain copies of some of my publications from my ftp directory: its address for anonymous ftp is ftp.uwm.edu and the directory is pub/Math/adbell (It currently contains postscript and dvi versions of some recent papers.)
If you want to know more about the Algebra group at UWM, follow this link