Theorems · Theorem · ring theory
AlgEquiv.ext
∀ {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] {f g : A₁ ≃ₐ[R] A₂}, (∀ (a : A₁), f a = g a) → f = g- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- AlgEquivstatement and proof · cited by 1,681
- DFunLike.extproof · cited by 240
Cited by60
Results whose statement or proof uses this declaration.
- AlgEquiv.ext_iffproof · cited by 8
- AlgEquiv.coe_toAlgHom_injectiveproof · cited by 8
- Polynomial.Gal.extproof · cited by 5
- ContinuousAlgEquiv.extproof · cited by 3
- Ideal.quotientEquivAlgOfEq_symmproof · cited by 3
- IsScalarTower.AlgEquiv.restrictNormalHom_compproof · cited by 2
- IsFractionRing.fieldEquivOfAlgEquivHom_injectiveproof · cited by 2
- AlgEquiv.toLinearEquiv_injectiveproof · cited by 2
- NumberField.InfinitePlace.mem_stabilizer_mk_iffproof · cited by 2
- MonoidAlgebra.mapAlgEquiv_transproof · cited by 1
- AlgEquiv.restrictNormalHom_idproof · cited by 1
- AlgEquiv.restrictNormal_transproof · cited by 1