Integral Closure
A valuation ring is integrally closed. Here, an integral domain D which is integrally closed in its field of fractions is said to be integrally closed. This means that if a member x of the field of fractions F of D satisfies an equation of the form xn + a1xn−1 + ... + a0 = 0, where the coefficients ai are elements of D, then x is in D.
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