Theorems · Theorem · commutative algebra

Polynomial.Bivariate.aeval_aeval_eq_aeval_algEquivAdjoin

∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {B : Type u_3}
  [inst_3 : CommRing B] [inst_4 : Algebra A B] [inst_5 : Algebra R B] [IsScalarTower R A B] {x : A} (y : B)
  (hx : Transcendental R x) (p : Polynomial (Polynomial R)),
  (Polynomial.aeval ((algebraMap A B) x)) ((Polynomial.aeval (Polynomial.C ⟨y, ⋯⟩)) p) =
    (Polynomial.aeval y) ((Polynomial.Bivariate.Transcendental.algEquivAdjoin hx) p)

Defined in

Mathlib.RingTheory.Adjoin.Polynomial.Bivariate

Cited by

1 results in Mathlib

Foundations

Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower