Theorems · Theorem · commutative algebra
Ideal.radical_mono
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R}, I ≤ J → I.radical ≤ J.radical- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 78 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.
Cites3
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
- Ideal.radicalstatement and proof · cited by 121
Cited by10
Results whose statement or proof uses this declaration.
- Ideal.IsRadical.radical_le_iffproof · cited by 5
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- Ideal.radical_infproof · cited by 5
- associatedPrimes.subset_union_of_exactproof · cited by 2
- Ideal.radical_mulproof · cited by 2
- Ideal.radical_supproof · cited by 1
- IsAssociatedPrime.eq_radicalproof · cited by 1
- Submodule.IsPrimary.radical_colon_singleton_of_notMemproof · cited by 1
- Ideal.radical_iInf_leproof · cited by 1
- Ideal.IsMinimalPrimaryDecomposition.minimalPrimes_subset_image_radicalproof · cited by 0