Theorems · Theorem · commutative algebra
Ideal.FG.isNilpotent_iff_le_nilradical
∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R}, I.FG → (IsNilpotent I ↔ I ≤ nilradical R)- Defined in
- Mathlib.RingTheory.Noetherian.Nilpotent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 4,748
- IsNilpotentstatement and proof · cited by 248
- le_bot_iffproof · cited by 116
- Ideal.FGstatement and proof · cited by 99
- nilradicalstatement and proof · cited by 41
- Ideal.pow_mem_powproof · cited by 19
- Ideal.exists_pow_le_of_le_radical_of_fgproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- isArtinianRing_iff_isNilpotent_maximalIdealproof · cited by 1
- Module.finite_of_surjective_of_ker_le_nilradicalproof · cited by 0