Back Normale Erweiterung German Extensión normal Spanish Normaali laajennus Finnish Extension normale French הרחבה נורמלית HE Estensione normale Italian 正規拡大 Japanese 정규 확대 Korean Rozszerzenie normalne Polish Extensão normal Portuguese
In abstract algebra, a normal extension is an algebraic field extension L/K for which every irreducible polynomial over K that has a root in L splits into linear factors in L.[1][2] This is one of the conditions for an algebraic extension to be a Galois extension. Bourbaki calls such an extension a quasi-Galois extension. For finite extensions, a normal extension is identical to a splitting field.
- ^ Lang 2002, p. 237, Theorem 3.3, NOR 3.
- ^ Jacobson 1989, p. 489, Section 8.7.