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Theorems · Definition · commutative algebra

IsLocalRing.ResidueField.mapEquiv

{R : Type u_1} →
  {S : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : IsLocalRing R] →
        [inst_2 : CommRing S] →
          [inst_3 : IsLocalRing S] → R ≃+* S → IsLocalRing.ResidueField R ≃+* IsLocalRing.ResidueField S

A ring isomorphism defines an isomorphism of residue fields.

Defined in
Mathlib.RingTheory.LocalRing.ResidueField.Basic
Cited by
5 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsLocalRingCommRingIsLocalRing
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Around this declaration

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

AlgebraicGeometry.Scheme.Spec.residueFieldIso · cited by 7Spec.residueFieldIsoIsLocalRing.ResidueField.mapAlgEquiv · cited by 1ResidueField.mapAlgEquivIsLocalRing.ResidueField.mapAut · cited by 1ResidueField.mapAutIsLocalRing.ResidueField.mapEquiv_trans · cited by 0ResidueField.mapEquiv_tra…Ideal.residueFieldRingEquiv · cited by 0Ideal.residueFieldRingEqu…IsLocalRing.ResidueField.mapEquiv_apply · cited by 0ResidueField.mapEquiv_app…IsLocalRing.ResidueField.mapAut_apply · cited by 0ResidueField.mapAut_applyIsLocalRing.ResidueField.mapEquiv.symm · cited by 0mapEquiv.symmIsLocalRing.ResidueField.mapEquiv_refl · cited by 0ResidueField.mapEquiv_reflDFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingRingEquiv · cited by 1147RingEquivRingHomClass.toRingHom · cited by 746RingHomClass.toRingHomRingEquiv.symm · cited by 567RingEquiv.symmIsLocalRing · cited by 339IsLocalRingIsLocalRing.ResidueField · cited by 156IsLocalRing.ResidueFieldIsLocalRing.ResidueField.map · cited by 16ResidueField.mapResidueField.mapEquivCITED BYCITES

Cites8

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

Cited by9

Results whose statement or proof uses this declaration.