Theorems · Theorem · commutative algebra
exists_maximalIdeal_pow_eq_of_principal
∀ (R : Type u_1) [inst : CommRing R] [IsNoetherianRing R] [inst_2 : IsLocalRing R] [IsDomain R], Submodule.IsPrincipal (IsLocalRing.maximalIdeal R) → ∀ (I : Ideal R), I ≠ ⊥ → ∃ n, I = IsLocalRing.maximalIdeal R ^ n
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites62
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
- Top.topproof · cited by 9,680
- Fieldproof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- mul_oneproof · cited by 3,885
- Unitsproof · cited by 2,804
- Multisetproof · cited by 2,627
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- le_antisymmproof · cited by 2,068
- Units.valproof · cited by 1,966
Cited by1
Results whose statement or proof uses this declaration.
- tfae_of_isNoetherianRing_of_isLocalRing_of_isDomainproof · cited by 1