Theorems · Definition · ring theory
TwoSidedIdeal.unop
{R : Type u_1} → [inst : NonUnitalNonAssocRing R] → TwoSidedIdeal Rᵐᵒᵖ → TwoSidedIdeal RIf I is a two-sided ideal of Rᵐᵒᵖ, then {x.unop | x ∈ I} is a two-sided ideal in R.
- Defined in
- Mathlib.RingTheory.TwoSidedIdeal.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- NonUnitalNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulOppositestatement and proof · cited by 1,135
- NonUnitalNonAssocRingstatement and proof · cited by 354
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.ringConproof · cited by 40
- RingCon.unopproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- TwoSidedIdeal.opOrderIsoproof · cited by 2
- TwoSidedIdeal.mem_unop_iffstatement · cited by 1
- TwoSidedIdeal.opOrderIso_symm_applystatement · cited by 0
- TwoSidedIdeal.coe_unopstatement · cited by 0
- TwoSidedIdeal.unop_ringConstatement and proof · cited by 0