Theorems · Theorem · commutative algebra
EuclideanDomain.divRadical_mul
∀ {E : Type u_1} [inst : EuclideanDomain E] [inst_1 : NormalizationMonoid E] [inst_2 : UniqueFactorizationMonoid E]
{a b : E},
IsCoprime a b → EuclideanDomain.divRadical (a * b) = EuclideanDomain.divRadical a * EuclideanDomain.divRadical b- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 2 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsCoprimestatement and proof · cited by 321
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- EuclideanDomainstatement and proof · cited by 124
- mul_mul_mul_commproof · cited by 65
- UniqueFactorizationMonoid.radicalproof · cited by 64
- EuclideanDomain.divRadicalstatement and proof · cited by 12
- EuclideanDomain.radical_mul_divRadicalproof · cited by 5
- IsCoprime.isRelPrimeproof · cited by 3
- UniqueFactorizationMonoid.radical_mulproof · cited by 2
- EuclideanDomain.eq_divRadicalproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- divRadical_dvd_derivativeproof · cited by 1
- Polynomial.abcproof · cited by 0