Theorems · Theorem · number theory

baseChange_ext_iff

∀ {R : Type uR} {A : Type uA} {M₂ : Type uM₂} {N₁ : Type uN₁} [inst : CommRing R] [inst_1 : CommRing A]
  [inst_2 : AddCommGroup M₂] [inst_3 : AddCommGroup N₁] [inst_4 : Algebra R A] [inst_5 : Module R N₁]
  [inst_6 : Module A N₁] [IsScalarTower R A N₁] [inst_8 : Module R M₂]
  {Q₁ Q₂ : QuadraticMap A (TensorProduct R A M₂) N₁}, Q₁ = Q₂ ↔ ∀ (m : M₂), Q₁ (1 ⊗ₜ[R] m) = Q₂ (1 ⊗ₜ[R] m)

Defined in

Mathlib.LinearAlgebra.QuadraticForm.TensorProduct

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Quot.sound

Assumes

CommRingCommRingAddCommGroupAddCommGroupAlgebraModuleModuleIsScalarTowerModule