Theorems · Theorem · commutative algebra
EuclideanDomain.divRadical_isUnit
∀ {E : Type u_1} [inst : EuclideanDomain E] [inst_1 : NormalizationMonoid E] [inst_2 : UniqueFactorizationMonoid E]
{u : E}, IsUnit u → IsUnit (EuclideanDomain.divRadical u)- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsUnitstatement and proof · cited by 1,602
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- EuclideanDomainstatement and proof · cited by 124
- EuclideanDomain.divRadicalstatement · cited by 12
- EuclideanDomain.div_oneproof · cited by 5
- UniqueFactorizationMonoid.radical_of_isUnitproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- divRadical_dvd_derivativeproof · cited by 1