Theorems · Theorem · field theory

minpoly.aeval_of_isScalarTower

∀ (R : Type u_3) {K : Type u_4} {T : Type u_5} {U : Type u_6} [inst : CommRing R] [inst_1 : Field K]
  [inst_2 : CommRing T] [inst_3 : Algebra R K] [inst_4 : Algebra K T] [inst_5 : Algebra R T] [IsScalarTower R K T]
  [inst_7 : CommSemiring U] [inst_8 : Algebra K U] [inst_9 : Algebra R U] [IsScalarTower R K U] (x : T) (y : U),
  (Polynomial.aeval y) (minpoly K x) = 0 → (Polynomial.aeval y) (minpoly R x) = 0

If y is a conjugate of x over a field K, then it is a conjugate over a subring R.

Defined in

Mathlib.FieldTheory.Minpoly.Field

Cited by

2 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldCommRingAlgebraAlgebraAlgebraIsScalarTowerCommSemiringAlgebraAlgebraIsScalarTower