Theorems · Theorem · ring theory
AlgEquiv.ext_iff
∀ {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}, f = g ↔ ∀ (a : A₁), f a = g a- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 23 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
- AlgEquiv.extproof · cited by 60
Cited by8
Results whose statement or proof uses this declaration.
- IsGaloisGroup.mulEquivCongr_apply_smulproof · cited by 3
- IsFractionRing.fieldEquivOfAlgEquivHom_injectiveproof · cited by 2
- IsFractionRing.stabilizerHom_surjectiveproof · cited by 2
- FixedPoints.toAlgAut_surjectiveproof · cited by 1
- isSolvable_of_isScalarTowerproof · cited by 1
- Polynomial.Gal.restrictProd_injectiveproof · cited by 1
- MulSemiringAction.toAlgEquiv_injectiveproof · cited by 0
- IntermediateField.restrictRestrictAlgEquivMapHom_injectiveproof · cited by 0