Theorems · Theorem · field theory

IsConjRoot.of_isScalarTower

∀ {K : Type u_2} {L : Type u_3} {S : Type u_4} [inst : CommRing S] [inst_1 : Field K] [inst_2 : Field L]
  [inst_3 : Algebra K S] [inst_4 : Algebra K L] [inst_5 : Algebra L S] [IsDomain S] [IsScalarTower K L S] {x y : S},
  IsIntegral K x → IsConjRoot L x y → IsConjRoot K x y

Let S / L / K be a tower of extensions. For any two elements y and x in S, if y is a conjugate root of x over L, then y is also a conjugate root of x over K.

Defined in

Mathlib.FieldTheory.Minpoly.IsConjRoot

Cited by

1 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldFieldAlgebraAlgebraAlgebraIsDomainIsScalarTower