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)
“Beat! beat! drums!—blow! bugles! blow!
Through the windows—through doors—burst like a ruthless force,
Into the solemn church, and scatter the congregation;
Into the school where the scholar is studying;
Leave not the bridegroom quiet—no happiness must he have now with his bride;
Nor the peaceful farmer any peace, plough his field or gathering his
grain;
So fierce you whirr and pound, you drums—so shrill you bugles blow.”
—Walt Whitman (1819–1892)