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Seminario: “Overrings of ultrapowers of rings”

Mercoledì 11 Luglio 2018, ore 15:30 - Aula 1BC50 - Alan Loper

ARGOMENTI: Seminari

Mercoledì 11 Luglio 2018 alle ore 15:30 in Aula 1BC50, Alan Loper (Ohio State University, Colombus, Ohio) terrà un seminario dal titolo “Overrings of ultrapowers of rings”.

Abstract
Let D be an integral domain. We look at two constructions of rings involving ultrapowers. Choose a nonprrincipal ultrafilter U of the set of natural numbers. In general, an ultrapower of D has too many prime ideals to reasonably study. We aim to build some overrings that are more accessible. First, suppose that D has an infinite number of maximal ideals. For each maximal ideal M of D use U to construct an ultrapower of D_M. Then intersect the ultrapowers. Second, let D be a local integrally closed domain which is not a valuation domain. Let {V_i} be a collection of valuation overrings of D which intersect to V. Use U to build an ultrapower of each V_i and intersect the ultrapowers. We examine the ideal structure of these to classes of overrings.