Theorems · Theorem · commutative algebra

Algebra.SubmersivePresentation.sum_jacobianRelationsOfHasCoeffs_mul_relationOfHasCoeffs

∀ {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] [inst_3 : Finite σ] (P : Algebra.SubmersivePresentation R S ι σ) (R₀ : Type u_5)
  [inst_4 : CommRing R₀] [inst_5 : Algebra R₀ R] [inst_6 : Algebra R₀ S] [inst_7 : IsScalarTower R₀ R S]
  [inst_8 : P.HasCoeffs R₀] [FaithfulSMul R₀ R] [inst_10 : Fintype σ],
  ∑ i, P.jacobianRelationsOfHasCoeffs R₀ i * Algebra.Presentation.relationOfHasCoeffs R₀ i =
    P.jacobianOfHasCoeffs R₀ * P.invJacobianOfHasCoeffs R₀ - 1

Defined in

Mathlib.RingTheory.Extension.Presentation.Core

Cited by

0 results in Mathlib

Foundations

Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFiniteCommRingAlgebraAlgebraIsScalarTowerAlgebra.SubmersivePresentation.HasCoeffsFaithfulSMulFintype