Theorems · Theorem · ring theory
RingEquiv.surjective
∀ {R : Type u_4} {S : Type u_5} [inst : Mul R] [inst_1 : Mul S] [inst_2 : Add R] [inst_3 : Add S] (e : R ≃+* S),
Function.Surjective ⇑e- Defined in
- Mathlib.Algebra.Ring.Equiv
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingEquivstatement and proof · cited by 1,147
- EquivLike.surjectiveproof · cited by 24
Cited by28
Results whose statement or proof uses this declaration.
- ringKrullDim_eq_of_ringEquivproof · cited by 9
- RingEquiv.finiteproof · cited by 5
- RingHom.surjective_respectsIsoproof · cited by 4
- RingHom.EssFiniteType.respectsIsoproof · cited by 2
- RingHom.finitePresentation_respectsIsoproof · cited by 2
- RingEquiv.isArtinianRingproof · cited by 2
- RingEquiv.isLocalRingproof · cited by 2
- RingEquiv.surjectiveOnStalksproof · cited by 2
- RingHom.FormallyUnramified.respectsIsoproof · cited by 2
- RingEquiv.height_comapproof · cited by 1
- Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrderedproof · cited by 1
- AlgebraicGeometry.IsClosedImmersion.Spec_iffproof · cited by 1