Theorems · Theorem · commutative algebra

Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val

∀ {R : Type u_1} {S : Type u_2} {ι : Type u_3} {σ : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
  [inst_2 : Algebra R S] {P : Algebra.Presentation R S ι σ} (R₀ : Type u_5) [inst_3 : CommRing R₀]
  [inst_4 : Algebra R₀ R] [inst_5 : Algebra R₀ S] [inst_6 : IsScalarTower R₀ R S] [inst_7 : P.HasCoeffs R₀]
  (x : MvPolynomial ι R₀),
  (P.tensorModelOfHasCoeffsInv R₀) ((MvPolynomial.aeval P.val) x) =
    1 ⊗ₜ[R₀] (Ideal.Quotient.mk (Ideal.span (Set.range (Algebra.Presentation.relationOfHasCoeffs R₀)))) x

Defined in

Mathlib.RingTheory.Extension.Presentation.Core

Cited by

2 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTowerAlgebra.Presentation.HasCoeffs