It is a splitting field of Here denotes any th primitive root of unity. The field is the normal closure (see below) of Normal closure If K is a field and L is an algebraic extension of K, then there is some algebraic extension M of L such that M is a normal extension of K. Furthermore, up to isomorphism there is only one such extension which is minimal, that is, the only subfield of M which contains L and which is a normal extension of K is M itself. This extension is called the normal closure of the extension L of K. If L is a finite extension of K, then its normal closure is also a finite extension. See also Galois extension Normal basis Citations References Field extensions