A splitting field of a polynomial p(X) over a field K is a field extension L of K over which p factors into linear factors
and such that the coefficients ai generate L over K. The extension L is then an extension of minimal degree over K in which p splits. It can be shown that such splitting fields exist and are unique up to isomorphism. The amount of freedom in that isomorphism is known to be the Galois group of p (if we assume it is separable).
Read more about Splitting Field: Facts
Famous quotes containing the words splitting and/or field:
“Verily, chemistry is not a splitting of hairs when you have got half a dozen raw Irishmen in the laboratory.”
—Henry David Thoreau (1817–1862)
“... many American Jews have a morbid tendency to exaggerate their handicaps and difficulties. ... There is no doubt that the Jew ... has to be twice as good as the average non- Jew to succeed in many a field of endeavor. But to dwell upon these injustices to the point of self-pity is to weaken the personality unnecessarily. Every human being has handicaps of one sort or another. The brave individual accepts them and by accepting conquers them.”
—Agnes E. Meyer (1887–1970)