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We introduce and explore the Uniform Izumi-Rees Property in Noetherian rings with applications to multiplicity theory and containment relationships among symbolic powers of ideals. As an application, we prove that if R is a normal domain essentially of finite type over a field, there exists a constant C so that for all prime ideals p q (R), if p q^ (t), then for all n, there is a containment of symbolic powers p^ (Cn) q^ (tn).
Thomas Polstra (Sun,) studied this question.