Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.radical_of_isUnit
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
{a : M}, IsUnit a → UniqueFactorizationMonoid.radical a = 1- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 3 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.
- IsUnitstatement and proof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.radicalstatement · cited by 64
- associated_one_iff_isUnitproof · cited by 14
- UniqueFactorizationMonoid.radical_oneproof · cited by 5
- UniqueFactorizationMonoid.radical_eq_of_associatedproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.exists_dvd_pow_iff_radical_dvdproof · cited by 1
- EuclideanDomain.divRadical_isUnitproof · cited by 1
- UniqueFactorizationMonoid.radical_eq_one_iffproof · cited by 0