Theorems · Theorem · ring theory

GradedAlgHom.cancel_left

∀ {R : Type u_1} {A : Type u_6} {B : Type u_7} {C : Type u_8} {ι : Type u_10} [inst : CommSemiring R]
  [inst_1 : Semiring A] [inst_2 : Semiring B] [inst_3 : Semiring C] [inst_4 : Algebra R A] [inst_5 : Algebra R B]
  [inst_6 : Algebra R C] [inst_7 : DecidableEq ι] [inst_8 : AddMonoid ι] {𝒜 : ι → Submodule R A} {ℬ : ι → Submodule R B}
  {𝒞 : ι → Submodule R C} [inst_9 : GradedAlgebra 𝒜] [inst_10 : GradedAlgebra ℬ] [inst_11 : GradedAlgebra 𝒞]
  {g₁ g₂ : 𝒜 →ₐᵍ[R] ℬ} {f : ℬ →ₐᵍ[R] 𝒞}, Function.Injective ⇑f → (f.comp g₁ = f.comp g₂ ↔ g₁ = g₂)

Defined in

Mathlib.RingTheory.GradedAlgebra.AlgHom

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringSemiringSemiringAlgebraAlgebraAlgebraDecidableEqAddMonoidGradedAlgebraGradedAlgebraGradedAlgebra