Theorems · Definition · commutative algebra
TwoSidedIdeal.jacobson
{R : Type u} → [inst : Ring R] → TwoSidedIdeal R → TwoSidedIdeal RThe Jacobson radical of I is the infimum of all maximal (left) ideals containing I.
- Defined in
- Mathlib.RingTheory.Jacobson.Ideal
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- TwoSidedIdealstatement and proof · cited by 151
- Ideal.jacobsonproof · cited by 88
- TwoSidedIdeal.asIdealproof · cited by 13
- Ideal.toTwoSidedproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- TwoSidedIdeal.asIdeal_jacobsonstatement · cited by 1
- TwoSidedIdeal.jacobson_matrixstatement and proof · cited by 1
- TwoSidedIdeal.mem_jacobson_iffstatement · cited by 0
- TwoSidedIdeal.matrix_jacobson_botstatement · cited by 0