Discrete valuations centered on local domains. (English) Zbl 1094.13502

Summary: 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 S. Izumi’s theorem [Publ. Res. Inst. Math. Sci. 21, 719–735 (1985; Zbl 0587.32016)] 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-fiberedness, and a valuative criterion for when the normal cone of an ideal in an integrally closed domain is reduced.


13A18 Valuations and their generalizations for commutative rings
13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13F40 Excellent rings


Zbl 0587.32016
Full Text: DOI


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