Theorems · Theorem · commutative algebra
Ideal.exists_radical_pow_le_of_fg
∀ {R : Type u_3} [inst : CommSemiring R] (I : Ideal R), I.radical.FG → ∃ n, I.radical ^ n ≤ I- Defined in
- Mathlib.RingTheory.Finiteness.Ideal
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 79 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.
Cites26
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
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- Submodule.spanproof · cited by 1,504
- Finset.rangeproof · cited by 1,341
- Nat.chooseproof · cited by 494
- le_or_gtproof · cited by 269
- Submodule.FGproof · cited by 230
- Set.singleton_subset_iffproof · cited by 206
- Set.mem_singletonproof · cited by 183
- Ideal.radicalstatement and proof · cited by 121
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.exists_eq_colon_of_mem_minimalPrimesproof · cited by 1
- IsNoetherianRing.isNilpotent_nilradicalproof · cited by 1
- maximalIdeal_isPrincipal_of_isDedekindDomainproof · cited by 1
- Ideal.exists_pow_le_of_le_radical_of_fg_radicalproof · cited by 0