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

Lorenzo Guerrieri (), William Heinzer (), Bruce Olberding () and Matthew Toeniskoetter ()
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Lorenzo Guerrieri: Università di catania
William Heinzer: Purdue University, Department of Mathematics
Bruce Olberding: New Mexico State University, Department of Mathematical Sciences
Matthew Toeniskoetter: Purdue University, Department of Mathematics

A chapter in Rings, Polynomials, and Modules, 2017, pp 257-280 from Springer

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

Keywords: Regular local ring; Local quadratic transform; Valuation ring; Pullback construction; 13H05; 13A15; 13A18 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-65874-2_13

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DOI: 10.1007/978-3-319-65874-2_13

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