Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772114 | Journal of Algebra | 2017 | 27 Pages |
Abstract
Let (R,m) be a regular local ring of dimension at least 2. Associated to each valuation domain birationally dominating R, there exists a unique sequence {Rn} of local quadratic transforms of R along this valuation domain. We consider the situation where the sequence {Rn}nâ¥0 is infinite, and examine ideal-theoretic properties of the integrally closed local domain S=ânâ¥0Rn. Among the set of valuation overrings of R, there exists a unique limit point V for the sequence of order valuation rings of the Rn. We prove the existence of a unique minimal proper Noetherian overring T of S, and establish the decomposition S=Tâ©V. If S is archimedean, then the complete integral closure Sâ of S has the form Sâ=Wâ©T, where W is the rank 1 valuation overring of V.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
William Heinzer, K. Alan Loper, Bruce Olberding, Hans Schoutens, Matthew Toeniskoetter,