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)
“After all the field of battle possesses many advantages over the drawing-room. There at least is no room for pretension or excessive ceremony, no shaking of hands or rubbing of noses, which make one doubt your sincerity, but hearty as well as hard hand-play. It at least exhibits one of the faces of humanity, the former only a mask.”
—Henry David Thoreau (1817–1862)