Theorems · Theorem · commutative algebra
IsNoetherianRing.isNilpotent_nilradical
∀ (R : Type u_1) [inst : CommSemiring R] [IsNoetherianRing R], IsNilpotent (nilradical R)
- Defined in
- Mathlib.RingTheory.Noetherian.Nilpotent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIsNoetherianRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement · cited by 4,748
- Bot.botproof · cited by 4,720
- IsNoetherianRingstatement and proof · cited by 268
- IsNilpotentstatement · cited by 248
- eq_bot_iffproof · cited by 159
- Ideal.radicalproof · cited by 121
- nilradicalstatement · cited by 41
- IsNoetherian.noetherianproof · cited by 32
- Ideal.exists_radical_pow_le_of_fgproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- IsNoetherianRing.isArtinianRing_of_krullDimLE_zeroproof · cited by 2