Theorems · Theorem · commutative algebra
Ideal.le_radical
∀ {R : Type u} [inst : CommSemiring R] {I : Ideal R}, I ≤ I.radical- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 77 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.
Cites4
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
- pow_oneproof · cited by 894
- Ideal.radicalstatement · cited by 121
Cited by16
Results whose statement or proof uses this declaration.
- Ideal.IsRadical.radical_le_iffproof · cited by 5
- Ideal.radical_eq_iffproof · cited by 2
- Ideal.radical_eq_jacobsonproof · cited by 2
- Ideal.IsPrime.isPrimaryproof · cited by 2
- AlgebraicGeometry.Proj.fromOfGlobalSections_preimage_basicOpenproof · cited by 2
- Ideal.disjoint_powers_iff_notMemproof · cited by 2
- associatedPrimes.subset_union_of_exactproof · cited by 2
- IsAssociatedPrime.annihilator_leproof · cited by 1
- Ideal.radical_supproof · cited by 1
- ModuleCat.exists_isRegular_of_exists_subsingleton_extproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.le_radicalproof · cited by 1
- Ideal.IsMinimalPrimaryDecomposition.minimalPrimes_subset_image_radicalproof · cited by 0