Theorems · Theorem · commutative algebra
IsArtinianRing.nilradical_pow_eq_iInf
∀ (R : Type u_1) [inst : CommRing R] [IsArtinianRing R] (n : ℕ), nilradical R ^ n = ⨅ I, I.asIdeal ^ n
- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsArtinianRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- SetLike.coeproof · cited by 8,199
- Fintypeproof · cited by 7,736
- Idealstatement and proof · cited by 4,748
- Set.rangeproof · cited by 4,705
- Finset.univproof · cited by 3,473
- iInfstatement and proof · cited by 1,690
- InfSet.sInfproof · cited by 935
- PrimeSpectrum.asIdealproof · cited by 333
- Fintype.ofFiniteproof · cited by 255
- iInf_congr_Propproof · cited by 218
Cited by4
Results whose statement or proof uses this declaration.
- IsArtinianRing.quotNilradicalPowEquivPiproof · cited by 2
- IsArtinianRing.nilradical_eq_iInfproof · cited by 2
- IsArtinianRing.quotNilradicalPowEquivPi_applystatement · cited by 0
- IsArtinianRing.quotNilradicalPowEquivPi_symm_applystatement and proof · cited by 0