Discrete valuations centered on local domains

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 Izumiʹs 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-fiberedness, and a valuative criterion for when the normal cone of an ideal in an integrally closed domain is reduced.