Theorems · Theorem · commutative algebra
IsArtinianRing.nilradical_eq_iInf
∀ (R : Type u_1) [inst : CommRing R] [IsArtinianRing R], nilradical R = iInf MaximalSpectrum.asIdeal
- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 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.
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
- iInfstatement and proof · cited by 1,690
- pow_oneproof · cited by 894
- IsArtinianRingstatement and proof · cited by 98
- MaximalSpectrumstatement and proof · cited by 73
- MaximalSpectrum.asIdealstatement and proof · cited by 58
- nilradicalstatement and proof · cited by 41
- IsArtinianRing.nilradical_pow_eq_iInfproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- IsArtinianRing.quotNilradicalEquivPiproof · cited by 2
- IsArtinianRing.quotNilradicalEquivPi_applystatement · cited by 0
- IsArtinianRing.quotNilradicalEquivPi_symm_applystatement and proof · cited by 0