Editing Normal extension (section)

==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 that is minimal, that is, the only subfield of ''M'' that contains ''L'' and that 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.