Theorems · Definition · ring theory
AlgEquiv.toEquiv
{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] → (A ≃ₐ[R] B) → A ≃ B- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Equivstatement · cited by 8,337
- AlgEquivstatement and proof · cited by 1,681
Cited by84
Results whose statement or proof uses this declaration.
- AlgEquiv.toAlgHomproof · cited by 273
- AlgEquiv.toRingEquivproof · cited by 137
- AlgEquiv.apply_symm_applyproof · cited by 67
- AlgEquiv.symm_apply_applyproof · cited by 36
- AlgEquiv.map_add'statement · cited by 19
- AlgEquiv.map_mul'statement · cited by 19
- IsGalois.card_aut_eq_finrankproof · cited by 16
- AlgEquiv.toMulEquivproof · cited by 13
- ContinuousAlgEquiv.toContinuousLinearEquivproof · cited by 12
- IsLocalization.isLocalization_of_algEquivproof · cited by 11
- AlgEquiv.symm_apply_eqproof · cited by 9
- ContinuousAlgEquiv.toHomeomorphproof · cited by 9