Mathlib Map

Theorems · Definition · ring theory

RingEquiv.toRingHom

{R : Type u_4} → {S : Type u_5} → [inst : NonAssocSemiring R] → [inst_1 : NonAssocSemiring S] → R ≃+* S → R →+* S

Reinterpret 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
Assumes
NonAssocSemiringNonAssocSemiring

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

starRingEnd · cited by 671starRingEndRingHom.RespectsIso · cited by 78RingHom.RespectsIsoHahnSeries.ofPowerSeries · cited by 45HahnSeries.ofPowerSeriesPolynomial.toLaurent · cited by 29Polynomial.toLaurentHomogeneousLocalization.awayMap · cited by 27HomogeneousLocalization.a…NumberField.FinitePlace.embedding · cited by 24FinitePlace.embeddingGradedRing.proj · cited by 23GradedRing.projRingHom.RespectsIso.cancel_right_isIso · cited by 18RespectsIso.cancel_right_…AlgebraicGeometry.IsAffineOpen.isLocalization_basicOpen · cited by 18IsAffineOpen.isLocalizati…IsGalois.card_aut_eq_finrank · cited by 16IsGalois.card_aut_eq_finr…RingHom.IsStableUnderBaseChange.mk · cited by 16IsStableUnderBaseChange.mkNumberField.InfinitePlace.Completion.extensionEmbedding · cited by 15Completion.extensionEmbed…RingHom.StableUnderComposition.respectsIso · cited by 15StableUnderComposition.re…RingEquiv.toMonoidHom · cited by 13RingEquiv.toMonoidHomAlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv · cited by 12AffineSpace.toSpecMvPolyI…RingHom · cited by 10189RingHomMonoidHom · cited by 3629MonoidHomAddMonoidHom · cited by 3230AddMonoidHomRingEquiv · cited by 1147RingEquivNonAssocSemiring · cited by 805NonAssocSemiringMulEquiv.toMonoidHom · cited by 126MulEquiv.toMonoidHomAddEquiv.toAddMonoidHom · cited by 101AddEquiv.toAddMonoidHomRingEquiv.toMulEquiv · cited by 26RingEquiv.toMulEquivRingEquiv.toAddEquiv · cited by 13RingEquiv.toAddEquivRingEquiv.toRingHomCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by191

Results whose statement or proof uses this declaration.