Mathlib Map

Theorems · Definition · ring theory

RingEquiv.mapTwoSidedIdeal

{R : Type u_1} →
  {S : Type u_2} →
    [inst : NonUnitalNonAssocRing R] → [inst_1 : NonUnitalNonAssocRing S] → R ≃+* S → TwoSidedIdeal R ≃o TwoSidedIdeal S

If R and S are isomorphic as rings, then two-sided ideals of R and two-sided ideals of S are order isomorphic.

Defined in
Mathlib.RingTheory.TwoSidedIdeal.Operations
Cited by
4 results in Mathlib
Foundations
Depth 48 from the axioms · uses propext, Quot.sound
Assumes
NonUnitalNonAssocRingNonUnitalNonAssocRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsSimpleRing.of_ringEquiv · cited by 0IsSimpleRing.of_ringEquivIsSimpleRing.of_surjective · cited by 0IsSimpleRing.of_surjectiveRingEquiv.mapTwoSidedIdeal_apply · cited by 0RingEquiv.mapTwoSidedIdea…RingEquiv.mapTwoSidedIdeal_symm · cited by 0RingEquiv.mapTwoSidedIdea…RingEquiv · cited by 1147RingEquivOrderIso · cited by 874OrderIsoRingEquiv.symm · cited by 567RingEquiv.symmNonUnitalNonAssocRing · cited by 354NonUnitalNonAssocRingTwoSidedIdeal · cited by 151TwoSidedIdealTwoSidedIdeal.comap · cited by 5TwoSidedIdeal.comapOrderIso.ofHomInv · cited by 3OrderIso.ofHomInvRingEquiv.mapTwoSidedIdealCITED BYCITES

Cites7

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

Cited by4

Results whose statement or proof uses this declaration.