KnowraField automorphismLinked fromLinked fromThe 7 pages that link to Field automorphism, each with the reason it gives.All 7Broader topic 1Related 5Narrower topic 1Galois groupBroader topic: Each element of a Galois group is an automorphism constrained to fix the base field.Galois theoryRelated: These structure-preserving symmetries form the groups at the heart of the theory.Splitting fieldRelated: Automorphisms fixing the base field permute the polynomial’s roots.Frobenius endomorphismNarrower topic: Frobenius is an automorphism only when it is surjective, as for perfect fields.Fundamental theorem of Galois theoryRelated: Automorphisms fixing the base field make up the Galois group.Primitive element theoremRelated: Automorphisms of a finite separable extension help distinguish its elements and describe its structure.Dieudonné's theoremRelated: Its action on scalars is the extra freedom allowed beyond ordinary linear transformations.