Theorems · Definition · ring theory
TwoSidedIdeal.op
{R : Type u_1} → [inst : NonUnitalNonAssocRing R] → TwoSidedIdeal R → TwoSidedIdeal RᵐᵒᵖIf I is a two-sided ideal of R, then {op x | x ∈ I} is a two-sided ideal in Rᵐᵒᵖ.
- 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 · cited by 1,135
- NonUnitalNonAssocRingstatement and proof · cited by 354
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.ringConproof · cited by 40
- RingCon.opproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- TwoSidedIdeal.opOrderIsoproof · cited by 2
- TwoSidedIdeal.mem_op_iffstatement · cited by 1
- TwoSidedIdeal.opOrderIso_applystatement · cited by 0
- TwoSidedIdeal.op_ringConstatement and proof · cited by 0
- TwoSidedIdeal.coe_opstatement · cited by 0