Theorems · Theorem · commutative algebra

Algebra.IsPushout.cancelBaseChange_tmul

∀ (R : Type u_1) (S : Type v₃) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (A : Type u_8)
  (B : Type u_9) [inst_3 : CommRing A] [inst_4 : CommRing B] [inst_5 : Algebra R A] [inst_6 : Algebra R B]
  [inst_7 : Algebra A B] [inst_8 : Algebra S B] [inst_9 : IsScalarTower R A B] [inst_10 : IsScalarTower R S B]
  [inst_11 : Algebra.IsPushout R S A B] (M : Type u_10) [inst_12 : AddCommGroup M] [inst_13 : Module R M]
  [inst_14 : Module A M] [inst_15 : IsScalarTower R A M] (m : M),
  (Algebra.IsPushout.cancelBaseChange R S A B M) (1 ⊗ₜ[A] m) = 1 ⊗ₜ[R] m

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerAlgebra.IsPushoutAddCommGroupModuleModuleIsScalarTower