Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.radical_prod
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
{ι : Type u_2} {f : ι → M} (s : Finset ι),
(↑s).Pairwise (Function.onFun IsRelPrime f) →
UniqueFactorizationMonoid.radical (∏ i ∈ s, f i) = ∏ i ∈ s, UniqueFactorizationMonoid.radical (f i)- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- Function.onFunstatement and proof · cited by 570
- Set.Pairwisestatement and proof · cited by 321
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Finset.consproof · cited by 221
- NormalizationMonoidstatement and proof · cited by 165
- IsRelPrimestatement and proof · cited by 136
- Finset.cons_inductionproof · cited by 85
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.