Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.radical_eq_of_associated
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
{a b : M}, Associated a b → UniqueFactorizationMonoid.radical a = UniqueFactorizationMonoid.radical b- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Finsetproof · cited by 13,712
- Finset.prodproof · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedstatement and proof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.radicalstatement and proof · cited by 64
- UniqueFactorizationMonoid.primeFactorsproof · cited by 32
- Associated.primeFactors_eqproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.radical_of_isUnitproof · cited by 3
- UniqueFactorizationDomain.radical_negproof · cited by 1
- UniqueFactorizationMonoid.radical_mul_of_isUnit_rightproof · cited by 0
- UniqueFactorizationMonoid.radical_mul_of_isUnit_leftproof · cited by 0