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A valuation theorem for Noetherian rings (2011.14749v2)
Published 30 Nov 2020 in math.AC and math.AG
Abstract: Let A and B be integral domains. Suppose A is Noetherian and B is a finitely generated A-algebra that contains A. Denote by A' the integral closure of A in B. We show that A' is determined by finitely many unique discrete valuation rings. Our result generalizes Rees' classical valuation theorem for ideals. We also obtain a variant of Zariski's main theorem.
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