Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.radical_associated
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
{a : M}, IsRadical a → a ≠ 0 → Associated (UniqueFactorizationMonoid.radical a) a- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetproof · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.prodproof · cited by 528
- Associatedstatement and proof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.radicalstatement · cited by 64
- UniqueFactorizationMonoid.primeFactorsproof · cited by 32
- UniqueFactorizationMonoid.prod_normalizedFactorsproof · cited by 23
- IsRadicalstatement and proof · cited by 16
- Finset.prod_valproof · cited by 5
- UniqueFactorizationMonoid.primeFactors_val_eq_normalizedFactorsproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsRadical.dvd_radicalproof · cited by 1