Patrick Smith (University of Glasgow, U.K.)
Title: "Ascending Chain Conditions in Groups, Rings and Modules

(Even Great Men Make Mistakes)"

Room: MW 154

Day/Date/Time: Tuesday, June 12, 2007 at 4:35 PM

Abstract:

The chain conditions in question are of the following type: given a positive integer n, an algebraic object satisfies the ascending chain condition on n-generated subobjects. For example, every free group satisfies the ascending chain condition on n-generated subgroups, for every positive integer n. If R is a right Noetherian ring then sometimes every free right R-module satisfies the ascending chain condition on n-generated submodules, for every positive integer n. This is a very non-technical talk intended for a wide audience. All you need to know is what  "Noetherian" means and some simple facts about Abelian groups.