Theorems · Theorem · ring theory
isArtinianRing_iff_isNilpotent_maximalIdeal
∀ (R : Type u_3) [inst : CommRing R] [IsNoetherianRing R] [inst_2 : IsLocalRing R], IsArtinianRing R ↔ IsNilpotent (IsLocalRing.maximalIdeal R)
- Defined in
- Mathlib.RingTheory.HopkinsLevitzki
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- IsNoetherianRingstatement and proof · cited by 268
- IsNilpotentstatement and proof · cited by 248
- List.TFAE.outproof · cited by 177
- IsArtinianRingstatement · cited by 98
- Ring.KrullDimLEproof · cited by 79
- le_antisymm_iffproof · cited by 62
- nilradicalproof · cited by 41
- IsNoetherian.noetherianproof · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes_of_isLocalRingproof · cited by 1