Theorems · Theorem · commutative algebra
Ideal.exists_pow_le_of_le_radical_of_fg_radical
∀ {R : Type u_3} [inst : CommSemiring R] {I J : Ideal R}, I ≤ J.radical → J.radical.FG → ∃ k, I ^ k ≤ J- Defined in
- Mathlib.RingTheory.Finiteness.Ideal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites7
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
- LE.le.transproof · cited by 3,151
- Ideal.radicalstatement and proof · cited by 121
- Ideal.FGstatement and proof · cited by 99
- Ideal.pow_right_monoproof · cited by 5
- Ideal.exists_radical_pow_le_of_fgproof · cited by 4
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