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• W2950188107 abstract "We consider infinite sequences {R_n} of successive local quadratic transforms of a regular local ring. Let S denote the directed union of the sequence of regular local rings R_n. We previously showed the existence of a unique limit point V of the family of order valuation rings of the sequence. In this paper, we examine asymptotic properties of this family of order valuations. We link this asymptotic behavior to ring-theoretic properties of S, namely whether S is archimedean and whether S is completely integrally closed. We construct examples of such S that are archimedean and completely integrally closed but not valuation domains. We give an explicit description of V, where the description depends on whether S is archimedean or non-archimedean." @default.
• W2950188107 created "2019-06-27" @default.
• W2950188107 creator A5000340762 @default.
• W2950188107 creator A5027558391 @default.
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• W2950188107 date "2015-09-24" @default.
• W2950188107 modified "2023-09-27" @default.
• W2950188107 title "Asymptotic properties of infinite directed unions of local quadratic transforms" @default.
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• W2950188107 hasPublicationYear "2015" @default.
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