Abstract
If R is a local integral domain let R + denote the integral closure of R in an algebraic closure of its quotient field. If z∈ R +, we would like to understand the conditions under which z∈ IR +, where I is an ideal of R. Necessary and sufficient conditions on the coefficients of the minimal irreducible polynomial for z are known when I is generated by two elements of a regular system of parameters and when z is in a degree two extension of R. In this article we obtain results for the case when z 3∈ R, as well as a sufficient condition for z to be in IR + when z a ∈ R for a⩾1 and I has a finite number of generators.
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