Theorems · Definition · ring theory
RingEquiv.ofBijective
{F : Type u_1} →
{R : Type u_4} →
{S : Type u_5} →
[inst : NonUnitalNonAssocSemiring R] →
[inst_1 : NonUnitalNonAssocSemiring S] →
[inst_2 : FunLike F R S] → [NonUnitalRingHomClass F R S] → (f : F) → Function.Bijective ⇑f → R ≃+* SProduce a ring isomorphism from a bijective ring homomorphism.
- Defined in
- Mathlib.Algebra.Ring.Equiv
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses Classical.choice
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.
- DFunLike.coestatement and proof · cited by 62,936
- Equivproof · cited by 8,337
- FunLikestatement and proof · cited by 2,560
- RingEquivstatement · cited by 1,147
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Function.Bijectivestatement and proof · cited by 863
- NonUnitalRingHomClassstatement and proof · cited by 82
- Equiv.ofBijectiveproof · cited by 70
Cited by43
Results whose statement or proof uses this declaration.
- frobeniusEquivproof · cited by 48
- AlgEquiv.ofBijectiveproof · cited by 34
- iterateFrobeniusEquivproof · cited by 28
- PerfectionMap.equivproof · cited by 7
- Module.Basis.algebraMapCoeffsproof · cited by 4
- NumberField.InfinitePlace.Completion.ringEquivComplexOfIsComplexproof · cited by 4
- NumberField.InfinitePlace.Completion.ringEquivRealOfIsRealproof · cited by 4
- quotAdjoinEquivQuotMapproof · cited by 3
- IsFractionRing.surjective_iff_isFieldproof · cited by 2
- RingHom.Flat.comp_iff_of_bijective_rightproof · cited by 2
- StarRingEquiv.ofBijectiveproof · cited by 2
- StarAlgEquiv.ofBijectiveproof · cited by 2