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, i.e. such that 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.
Read more about this topic: Normal Extension
Famous quotes containing the word normal:
“You have promise, Mlle. Dubois, but you must choose between an operatic career and what is usually called “a normal life.” Though why it is so called is beyond me.”
—Eric Taylor, Leroux, and Arthur Lubin. M. Villeneuve (Frank Puglia)