Theorems · Definition · commutative algebra
EuclideanDomain.divRadical
{E : Type u_1} → [inst : EuclideanDomain E] → [NormalizationMonoid E] → [UniqueFactorizationMonoid E] → E → EDivision of an element by its radical in a Euclidean domain.
- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- UniqueFactorizationMonoid.radicalproof · cited by 64
Cited by12
Results whose statement or proof uses this declaration.
- EuclideanDomain.radical_mul_divRadicalstatement · cited by 5
- divRadical_dvd_wronskian_leftstatement and proof · cited by 2
- EuclideanDomain.divRadical_dvd_selfstatement · cited by 2
- EuclideanDomain.divRadical_mulstatement and proof · cited by 2
- EuclideanDomain.divRadical_mul_radicalstatement and proof · cited by 1
- divRadical_dvd_derivativestatement and proof · cited by 1
- divRadical_dvd_wronskian_rightstatement and proof · cited by 1
- EuclideanDomain.eq_divRadicalstatement · cited by 1
- IsCoprime.divRadicalstatement and proof · cited by 1
- EuclideanDomain.divRadical_isUnitstatement · cited by 1
- EuclideanDomain.divRadical_ne_zerostatement · cited by 0
- Polynomial.abcproof · cited by 0