Theorems · Theorem · field theory

isConjRoot_iff_exists_algEquiv

∀ {K : Type u_2} {L : Type u_3} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] [Normal K L] {x y : L},
  IsConjRoot K x y ↔ ∃ σ, σ y = x

Let L / K be a normal field extension. For any two elements x and y in L, y is a conjugate root of x if and only if there exists a K-automorphism σ : Gal(L/K) such that σ y = x.

Defined in

Mathlib.FieldTheory.Minpoly.IsConjRoot

Cited by

2 results in Mathlib

Foundations

Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraNormal