Carmelo Finocchiaro, Universita' di Padova

Title: On a topological characterization of Pruefer v-multiplication rings

Abstract: Let D be an integral domain. It is well known that, if D is a PvMD, then D is an essential domain, that is, there is a collection V:={Vi : i ∈ I} of valuation overrings of D that are localizations of D such that D is the intersection of the Vi 's; such a collection V is called an essential representation of D. This condition is necessary but not sufficient for D to be a PvMD, as Heinzer and Ohm showed in [1].
In this talk we will present a new condition, topological in nature, on the centers of an essential representation of D in order to get that D is a PvMD, and we will describe several applications of this characterization.

[1] W. Heinzer, J. Ohm, An essential ring which is not a v-multiplication ring. Canad. J. Math. 25 (1973), 856–861.