Theorems · Definition · ring theory
RingEquiv.toRingHom
{R : Type u_4} → {S : Type u_5} → [inst : NonAssocSemiring R] → [inst_1 : NonAssocSemiring S] → R ≃+* S → R →+* SReinterpret a ring equivalence as a ring homomorphism.
- Defined in
- Mathlib.Algebra.Ring.Equiv
- Cited by
- 150 results in Mathlib
- Foundations
- Depth 21 from the axioms, rests on 154 definitions · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- MonoidHomproof · cited by 3,629
- AddMonoidHomproof · cited by 3,230
- RingEquivstatement and proof · cited by 1,147
- NonAssocSemiringstatement and proof · cited by 805
- MulEquiv.toMonoidHomproof · cited by 126
- AddEquiv.toAddMonoidHomproof · cited by 101
- RingEquiv.toMulEquivproof · cited by 26
- RingEquiv.toAddEquivproof · cited by 13
Cited by191
Results whose statement or proof uses this declaration.
- starRingEndproof · cited by 671
- RingHom.RespectsIsoproof · cited by 78
- HahnSeries.ofPowerSeriesproof · cited by 45
- Polynomial.toLaurentproof · cited by 29
- HomogeneousLocalization.awayMapproof · cited by 27
- NumberField.FinitePlace.embeddingproof · cited by 24
- GradedRing.projproof · cited by 23
- RingHom.RespectsIso.cancel_right_isIsoproof · cited by 18
- AlgebraicGeometry.IsAffineOpen.isLocalization_basicOpenproof · cited by 18
- IsGalois.card_aut_eq_finrankproof · cited by 16
- RingHom.IsStableUnderBaseChange.mkproof · cited by 16
- NumberField.InfinitePlace.Completion.extensionEmbeddingproof · cited by 15