Theorems · Theorem · field theory

isConjRoot_iff_orbitRel

∀ {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 ↔ (MulAction.orbitRel Gal(L/K) L) x y

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 x and y falls in the same orbit of the action of Galois group.

Defined in

Mathlib.FieldTheory.Minpoly.IsConjRoot

Cited by

0 results in Mathlib

Foundations

Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraNormal