Theorems · Theorem · ring theory
AlgHom.coe_ringHom_injective
∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B], Function.Injective RingHomClass.toRingHom- Defined in
- Mathlib.Algebra.Algebra.Hom
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- AlgHomstatement and proof · cited by 3,236
- RingHomClass.toRingHomstatement and proof · cited by 746
- AlgHom.coe_fn_injectiveproof · cited by 1
Cited by20
Results whose statement or proof uses this declaration.
- Ideal.ResidueField.algHom_extproof · cited by 7
- Polynomial.algHom_ext'proof · cited by 6
- Algebra.FormallySmooth.of_isLocalizationproof · cited by 6
- Algebra.FormallyUnramified.of_isLocalizationproof · cited by 5
- AdjoinRoot.algHom_ext'proof · cited by 2
- IsLocalization.algHom_extproof · cited by 2
- MvPolynomial.algHom_ext'proof · cited by 1
- IntermediateField.Lifts.nonempty_algHom_of_exist_lifts_finsetproof · cited by 1
- AlgHom.coe_addMonoidHom_injectiveproof · cited by 1
- NumberField.InfinitePlace.unramifedPlacesOver_ncard_add_eq_finrankproof · cited by 1
- IsPurelyInseparable.injective_restrictDomainproof · cited by 1
- AlgHom.coe_monoidHom_injectiveproof · cited by 1