Title: GCD property for Shannon extensions
Speaker: Lorenzo Guerrieri (University of Catania)
Abstract: Let $R$ be a regular local ring of dimension $d >1$. Recently, several authors studied the rings obtained as infinite directed union of iterated local quadratic transforms of $R$, and call them quadratic Shannon extensions.
Here we study features of directed union of local monoidal transforms of a regular local ring (monoidal Shannon extensions) and more in general of directed unions of GCD domains. In particular we are interested in understand when they still are GCD domains.