Seminar:  OSU-OU Ring Theory Seminar

Title: Quantified versions of some ring properties

Speaker:  Hans Schoutens

Day/Date: Friday, June 2, 2007

Time:     4:45 PM

Location: MW154

Abstract: in a domain, the product of two non-zero elements is non-zero. We may ask, how non-zero is this product? To measure this, at least in a local ring, we resort to the (canonical) adic norm of the ring. One can now classify those Noetherian local domains in which the norm of a product is bounded by the norms of the factors (this is due to Rees, with explicit

bounds given by Swanson and Hubl). I will present another proof using

ultraproducts. The advantage of this proof is that it can be generalized to other ring theoretic properties. However, this also requires a second

measure of the size of an element, which for want of a better name I will

call its cut-size (it is related to the multiplicity). Using these two

measures, we can now "quantify" certain ring-theoretic properties like being reduced, normal, ...