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
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