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Discrete valuations centered on local domains

✍ Scribed by Reinhold Hübl; Irena Swanson

Book ID
104152326
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
174 KB
Volume
161
Category
Article
ISSN
0022-4049

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✦ Synopsis

We study applications of discrete valuations to ideals in analytically irreducible domains, in particular, applications to zero divisors modulo powers of ideals. We prove a uniform version of Izumi's theorem and calculate several examples illustrating it, such as for rational singularities. The paper contains a new criterion of analytic irreducibility, a new criterion of one-ÿberedness, and a valuative criterion for when the normal cone of an ideal in an integrally closed domain is reduced.

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