Editing Normal extension (section)

{{Short description|Algebraic field extension}}
{{Other uses|Normal closure (disambiguation){{!}}Normal closure}}
In [[abstract algebra]], a '''normal extension''' is an [[Algebraic extension|algebraic field extension]] ''L''/''K'' for which every [[irreducible polynomial]] over ''K'' that has a [[zero of a function|root]] in ''L'' splits into linear factors over ''L''.{{sfn|Lang|2002|p=237|loc=Theorem 3.3, NOR 3}}{{sfn|Jacobson|1989|p=489|loc=Section 8.7}} This is one of the conditions for an algebraic extension to be a [[Galois extension]]. [[Nicolas Bourbaki|Bourbaki]] calls such an extension a '''quasi-Galois extension'''. For [[Finite extension|finite extensions]], a normal extension is identical to a [[splitting field]].