Seminario MALGA Padova Verona - Moduli Algebre Anelli: “On a topological characterization of Pruefer v-multiplication rings”

Mercoledì 12 Dicembre 2018, ore 16:15 - Sala Riunioni 702 - Carmelo Finocchiaro


Mercoledì 12 Dicembre 2018 alle ore 16:15 in Sala Riunioni 702, Carmelo Finocchiaro (Università di Padova) terrà un seminario dal titolo “On a topological characterization of Pruefer v-multiplication rings” nell'ambito del Seminario Padova-Verona MALGA - Moduli Algebre Anelli.

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 $V:=\{V_i : i \in I\}$ of valuation overrings of D that are localizations of D such that D is the intersection of the $V_i$'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.