Theorems · Theorem · commutative algebra

PowerBasis.equivOfRoot_map

∀ {S : Type u_2} [inst : Ring S] {A : Type u_4} [inst_1 : CommRing A] {S' : Type u_7} [inst_2 : CommRing S']
  [inst_3 : Algebra A S] [inst_4 : Algebra A S'] (pb : PowerBasis A S) (e : S ≃ₐ[A] S')
  (h₁ : (Polynomial.aeval pb.gen) (minpoly A (pb.map e).gen) = 0)
  (h₂ : (Polynomial.aeval (pb.map e).gen) (minpoly A pb.gen) = 0), pb.equivOfRoot (pb.map e) h₁ h₂ = e

Defined in

Mathlib.RingTheory.PowerBasis

Cited by

1 results in Mathlib

Foundations

Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingCommRingCommRingAlgebraAlgebra