Editing Normal extension (section)

== Definition ==
Let ''<math>L/K</math>'' be an algebraic extension (i.e., ''L'' is an algebraic extension of ''K''), such that <math>L\subseteq \overline{K}</math> (i.e., ''L'' is contained in an [[algebraic closure]] of ''K''). Then the following conditions, any of which can be regarded as a definition of '''normal extension''', are equivalent:{{sfn|Lang|2002|p=237|loc=Theorem 3.3}}
* Every [[Embedding (field theory)|embedding]] of ''L'' in <math>\overline{K}</math> over ''K'' induces an [[automorphism]] of ''L''.
* ''L'' is the [[splitting field]] of a family of polynomials in <math>K[X]</math>.
* Every irreducible polynomial of <math>K[X]</math> that has a root in ''L'' splits into linear factors in ''L''.