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Let \(\{R_{n},\mathfrak{m}_{n}\}_{n\geq 0}\) be an infinite sequence of regular local rings with R n+1 birationally dominating R n and \(\mathfrak{m}_{n}R_{n+1}\) a principal ideal of R n+1 for each n. We examine properties of the integrally closed local domain \(S =\bigcup _{n\geq 0}R_{n}\).

Directed Unions of Local Quadratic Transforms of Regular Local Rings and Pullbacks