Theorems · Theorem · commutative algebra
isLocalRing_of_isAdicComplete_maximal
∀ {R : Type u_1} [inst : CommRing R] (m : Ideal R) [m.IsMaximal] [IsAdicComplete m R], IsLocalRing R- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- Ideal.IsMaximalstatement and proof · cited by 452
- IsLocalRingstatement · cited by 339
- bot_leproof · cited by 306
- IsAdicCompletestatement and proof · cited by 124
- sInf_leproof · cited by 110
- Ideal.IsMaximal.ne_topproof · cited by 42
- Ideal.IsMaximal.eq_of_leproof · cited by 39
- IsLocalRing.of_unique_max_idealproof · cited by 4
- IsAdicComplete.le_jacobson_botproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AdicCompletion.isLocalRing_of_fgproof · cited by 4