Theorems · Theorem · ring theory
AlgEquiv.coe_toAlgHom_injective
∀ {R : Type uR} {A₁ : Type uA₁} {A₂ : Type uA₂} [inst : CommSemiring R] [inst_1 : Semiring A₁] [inst_2 : Semiring A₂]
[inst_3 : Algebra R A₁] [inst_4 : Algebra R A₂], Function.Injective AlgEquiv.toAlgHom- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
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.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement · cited by 3,236
- AlgEquivstatement and proof · cited by 1,681
- AlgEquiv.toAlgHomstatement and proof · cited by 273
- AlgEquiv.extproof · cited by 60
- AlgHom.congr_funproof · cited by 40
Cited by8
Results whose statement or proof uses this declaration.
- minpoly_algEquiv_toLinearMapproof · cited by 2
- DividedPowerAlgebra.mapEquiv_transproof · cited by 0
- IsPrimitiveRoot.autToPow_injectiveproof · cited by 0
- Algebra.TensorProduct.congr_reflproof · cited by 0
- Algebra.TensorProduct.congr_transproof · cited by 0
- Algebra.TensorProduct.lmulEquiv_eq_lidOfCompatibleSMulproof · cited by 0
- AlgEquiv.coe_algHom_injectiveproof · cited by 0
- DividedPowerAlgebra.mapEquiv_reflproof · cited by 0