Theorems · Theorem · commutative algebra
Ideal.exists_pow_le_of_le_radical_of_fg
∀ {R : Type u_3} [inst : CommSemiring R] {I J : Ideal R}, I ≤ J.radical → I.FG → ∃ n, I ^ n ≤ J- Defined in
- Mathlib.RingTheory.Finiteness.Ideal
- Cited by
- 2 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.
Cites15
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
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- Submodule.FGproof · cited by 230
- sup_leproof · cited by 159
- Ideal.radicalstatement and proof · cited by 121
- Ideal.FGstatement and proof · cited by 99
- Ideal.submodule_span_eqproof · cited by 25
Cited by2
Results whose statement or proof uses this declaration.
- PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopenproof · cited by 2
- Ideal.FG.isNilpotent_iff_le_nilradicalproof · cited by 2