Local properties of integral domains under extensions and pullback constructions

Abstract

For a property $\mathcal{X}$ of integral domains, an integral domain $D$ is said to be a {\it locally $\mathcal{X}$-domain} if $D_P$ has the property $\mathcal{X}$ for every prime ideal $P$ of $D$. In this paper, we study the transfer of local properties of integral domains under several extensions and constructions, including flat overrings, Nagata ideal transforms, polynomial rings and their quotient extensions, and pullback constructions.