Theorems · Theorem · commutative algebra
EuclideanDomain.radical_mul_divRadical
∀ {E : Type u_1} [inst : EuclideanDomain E] [inst_1 : NormalizationMonoid E] [inst_2 : UniqueFactorizationMonoid E]
{a : E}, UniqueFactorizationMonoid.radical a * EuclideanDomain.divRadical a = a- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 77 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.
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- EuclideanDomainstatement and proof · cited by 124
- mul_div_cancel_left₀proof · cited by 111
- UniqueFactorizationMonoid.radicalstatement and proof · cited by 64
- EuclideanDomain.divRadicalstatement · cited by 12
- EuclideanDomain.mul_div_assocproof · cited by 8
- UniqueFactorizationMonoid.radical_dvd_selfproof · cited by 7
- UniqueFactorizationMonoid.radical_ne_zeroproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- EuclideanDomain.divRadical_mulproof · cited by 2
- EuclideanDomain.divRadical_mul_radicalproof · cited by 1
- divRadical_dvd_derivativeproof · cited by 1
- IsCoprime.divRadicalproof · cited by 1
- EuclideanDomain.divRadical_ne_zeroproof · cited by 0