Theorems · Theorem · commutative algebra
Ideal.radical_sup
∀ {R : Type u} [inst : CommSemiring R] (I J : Ideal R), (I ⊔ J).radical = (I.radical ⊔ J.radical).radical- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 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.
Cites11
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_antisymmproof · cited by 2,068
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- sup_leproof · cited by 159
- Ideal.radicalstatement · cited by 121
- sup_le_supproof · cited by 48
- Ideal.le_radicalproof · cited by 16
- Ideal.radical_monoproof · cited by 10
- Ideal.radical_le_radical_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.radical_supproof · cited by 0