Integral closures of Noetherian integral domains as intersections

Call, Frederick W.

doi:10.1090/S0002-9939-1995-1227514-7

Integral closures of Noetherian integral domains as intersections
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by Frederick W. Call PDF

Proc. Amer. Math. Soc. 123 (1995), 1049-1052 Request permission

Abstract:

Three equivalent formulations of the property that the integral closure $\overline A$ of a noetherian domain A can be written as $\cap {\bar A_p}$ at all height-one primes p, are given in terms of PDE, ${A^{(1)}}$, and bad minimal primes in completions. Examples with these properties include excellent domains and domains with a canonical module. Writing $\overline A$ as an intersection of DVR’s is also addressed.

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