WEEKLY ACTIVITIES

Time: 9:00 - 9:45, Wednesday April 20, 2022

Abstract: An integral domain $D$ is said to be of Krull type if $D = cap D_v$ is a locally finite intersection of essential valuation overrings $D_v$ of $D$. If each $D_v$ is required to be one-dimensional and discrete, then $D$ is called a Krull domain. In this paper, we show that if $D = cap D_v$ is an integral domain of Krull type such that some $D_v$ is not an SFT ring, then the power series ring $D[![X]!]$ is not a locally finite intersection of valuation domains. This is a generalization of our previous work, where $D$ is assumed to be a valuation domain. It follows that $D[![X]!]$ is a Krull domain if and only if both $D$ and $D[![X]!]$ are integral domains of Krull type, which is an improvement of a result by Paran and Temkin. We also prove that if $D$ is a Pr"ufer domain, then $D[![X]!]$ is a Krull domain if and only if $D[![X]!]$ is an integral domain of Krull type.

Online: https://meet.google.com/esi-huxm-xqg