Theorems · Theorem · ring theory
GradedAlgHom.coe_algHom_injective
Deprecated since 2026-05-05Use GradedAlgHom.coe_toAlgHom_injective instead.
∀ {R : Type u_1} {A : Type u_6} {B : Type u_7} {ι : Type u_10} [inst : CommSemiring R] [inst_1 : Semiring A]
[inst_2 : Semiring B] [inst_3 : Algebra R A] [inst_4 : Algebra R B] [inst_5 : DecidableEq ι] [inst_6 : AddMonoid ι]
{𝒜 : ι → Submodule R A} {ℬ : ι → Submodule R B} [inst_7 : GradedAlgebra 𝒜] [inst_8 : GradedAlgebra ℬ],
Function.Injective GradedAlgHom.toAlgHomAlias of GradedAlgHom.coe_toAlgHom_injective.
- Defined in
- Mathlib.RingTheory.GradedAlgebra.AlgHom
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement · cited by 13,802
- Algebrastatement · cited by 11,388
- CommSemiringstatement · cited by 10,911
- Submodulestatement · cited by 7,192
- AlgHomstatement · cited by 3,236
- AddMonoidstatement · cited by 2,864
- GradedAlgebrastatement · cited by 97
- GradedAlgHomstatement · cited by 52
- GradedAlgHom.toAlgHomstatement · cited by 17
- GradedAlgHom.coe_toAlgHom_injectiveproof · cited by 7
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