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.
Read more about this topic: Valuation Ring
Famous quotes containing the word integral:
“An island always pleases my imagination, even the smallest, as a small continent and integral portion of the globe. I have a fancy for building my hut on one. Even a bare, grassy isle, which I can see entirely over at a glance, has some undefined and mysterious charm for me.”
—Henry David Thoreau (1817–1862)