Theorems · Theorem · commutative algebra
Ideal.radical_mul
∀ {R : Type u} [inst : CommSemiring R] (I J : Ideal R), (I * J).radical = I.radical ⊓ J.radical- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 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.
Cites9
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
- pow_addproof · cited by 315
- Ideal.radicalstatement and proof · cited by 121
- Ideal.mul_mem_mulproof · cited by 29
- Ideal.mul_le_infproof · cited by 10
- Ideal.radical_monoproof · cited by 10
- Ideal.radical_infproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isIrreducible_zeroLocus_iff_of_radicalproof · cited by 3
- AlgebraicGeometry.Scheme.IdealSheafData.radical_mulproof · cited by 0