Theorems · Theorem · ring theory
AlgEquiv.toAlgHom_toRingHom
∀ {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] (e : A₁ ≃ₐ[R] A₂), ↑↑e = ↑e- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 6 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
- RingHomstatement · cited by 10,189
- AlgHomstatement · cited by 3,236
- AlgEquivstatement and proof · cited by 1,681
- RingHomClass.toRingHomstatement · cited by 746
- AlgEquiv.toAlgHomstatement · cited by 273
Cited by6
Results whose statement or proof uses this declaration.
- Ideal.inertiaDeg'_comap_eqproof · cited by 2
- Ideal.ramificationIdx_smulproof · cited by 2
- Algebra.QuasiFiniteAt.exists_basicOpen_eq_singletonproof · cited by 2
- Ideal.ramificationIdx'_comap_eqproof · cited by 2
- NumberField.InfinitePlace.isUnramified_smul_iffproof · cited by 1
- Algebra.FinitePresentation.mvPolynomial_of_finitePresentationproof · cited by 0