Theorems · Theorem · commutative algebra
Ideal.jacobson_bot
∀ {R : Type u} [inst : Ring R], ⊥.jacobson = Ring.jacobson R- Defined in
- Mathlib.RingTheory.Jacobson.Ideal
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Submoduleproof · cited by 7,192
- Set.ofPredproof · cited by 6,101
- Idealstatement and proof · cited by 4,748
- Bot.botstatement · cited by 4,720
- InfSet.sInfproof · cited by 935
- Ideal.IsMaximalproof · cited by 452
- IsCoatomproof · cited by 114
- Ideal.jacobsonstatement · cited by 88
- Ring.jacobsonstatement · cited by 37
Cited by4
Results whose statement or proof uses this declaration.
- IsArtinianRing.isNilpotent_jacobson_botproof · cited by 4
- IsLocalRing.ringJacobson_eq_maximalIdealproof · cited by 4
- Ideal.ringJacobson_le_jacobsonproof · cited by 1
- IsArtinianRing.finite_of_compactSpace_of_t2Spaceproof · cited by 0