Theorems · Definition · ring theory
TwoSidedIdeal.orderIsoIsTwoSided
{R : Type u_1} → [inst : Ring R] → TwoSidedIdeal R ≃o { I // I.IsTwoSided }A two-sided ideal is simply a left ideal that is two-sided.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- OrderIsostatement · cited by 874
- Ideal.IsTwoSidedstatement and proof · cited by 179
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.asIdealproof · cited by 13
- Ideal.toTwoSidedproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- isSimpleRing_iff_isTwoSided_impproof · cited by 1
- TwoSidedIdeal.orderIsoIsTwoSided_apply_coestatement and proof · cited by 1
- TwoSidedIdeal.orderIsoIsTwoSided_symm_applystatement and proof · cited by 0