Theorems · Theorem · commutative algebra

PowerBasis.equivOfRoot_aeval

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

Defined in

Mathlib.RingTheory.PowerBasis

Cited by

2 results in Mathlib

Foundations

Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingCommRingAlgebraRingAlgebra