Theorems · Theorem · commutative algebra
EuclideanDomain.eq_divRadical
∀ {E : Type u_1} [inst : EuclideanDomain E] [inst_1 : NormalizationMonoid E] [inst_2 : UniqueFactorizationMonoid E]
{a x : E}, UniqueFactorizationMonoid.radical a * x = a → x = EuclideanDomain.divRadical a- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 1 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- EuclideanDomainstatement and proof · cited by 124
- UniqueFactorizationMonoid.radicalstatement and proof · cited by 64
- EuclideanDomain.divRadicalstatement · cited by 12
- EuclideanDomain.eq_div_of_mul_eq_leftproof · cited by 6
- UniqueFactorizationMonoid.radical_ne_zeroproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanDomain.divRadical_mulproof · cited by 2