Theorems · Theorem · commutative algebra
IsLocalRing.ringJacobson_eq_maximalIdeal
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsLocalRing R], Ring.jacobson R = IsLocalRing.maximalIdeal R
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement · cited by 4,748
- Bot.botproof · cited by 4,720
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement · cited by 297
- Ring.jacobsonstatement · cited by 37
- top_ne_botproof · cited by 15
- IsLocalRing.jacobson_eq_maximalIdealproof · cited by 10
- Ideal.jacobson_botproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDimproof · cited by 1
- ringKrullDim_quotSMulTop_succ_eq_ringKrullDimproof · cited by 0
- ringKrullDim_le_ringKrullDim_add_cardproof · cited by 0
- ringKrullDim_le_ringKrullDim_add_spanFinrankproof · cited by 0