Speaker: David E. Dobbs, University of Tennessee, Knoxville

Title: Classifying Minimal Ring Extensions

Abstract: Ideally, any scientist (and, in particular, any mathematician) wishes to classify the examples or instances of each concept that s/he is studying. Here, “to classify” means giving a list that contains exactly one isomorphic copy of each such instance. In this talk, we accomplish a classification in this sense for the concept of “minimal ring extension” of an arbitrary integral domain. Minimal ring extensions can be thought of as the basic building blocks of arbitrary ring extensions and, thus, are of wide use in both pure mathematics and applications. Classifying minimal ring extensions can be thought of a building a periodic table for ring extensions. Prior to May 2005, such a classification had been accomplished only for the minimal ring extensions of a field (by Daniel Ferrand and Jean-Pierre Olivier in 1970). This talk will describe the work of the speaker since May 2005, some of which was in collaboration with Professor Jay Shapiro (of George Mason University), that led to the classification of the minimal ring extensions of any integral domain (and beyond). The first half of the talk will provide enough background to make the entire talk accessible to any student or faculty member whose understanding of abstract algebra is at least at the honors senior undergraduate level. The second half of the talk will summarize some of the papers written on the subject since May 2005.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491