KnowraNormal extensionLinked fromLinked fromThe 6 pages that link to Normal extension, each with the reason it gives.All 6Broader topic 1Related 5Field extensionBroader topic: Normality describes when polynomial roots arrive together inside the extension.Galois groupRelated: Normality ensures base-field embeddings carry the extension onto itself, giving automorphisms.Galois theoryRelated: Normality makes embeddings of the extension correspond to its automorphisms.Splitting fieldRelated: A splitting field is normal over its base field when the polynomial is irreducible.Fundamental theorem of Galois theoryRelated: Normality, together with separability, supplies the theorem’s Galois hypothesis.Kronecker–Weber theoremRelated: Finite abelian extensions of the rationals are Galois, hence normal.