Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.isRadical_radical
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
{a : M}, IsRadical (UniqueFactorizationMonoid.radical a)- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsproof · cited by 151
- Dvd.dvd.transproof · cited by 148
- UniqueFactorizationMonoid.radicalstatement and proof · cited by 64
- UniqueFactorizationMonoid.primeFactorsproof · cited by 32
- UniqueFactorizationMonoid.prime_of_normalized_factorproof · cited by 23
- UniqueFactorizationMonoid.dvd_of_mem_normalizedFactorsproof · cited by 20
- IsRadicalstatement · cited by 16
- UniqueFactorizationMonoid.irreducible_of_normalized_factorproof · cited by 15
- UniqueFactorizationMonoid.normalizedFactors_zeroproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.radical_dvd_iff_primeFactors_subsetproof · cited by 1
- UniqueFactorizationMonoid.squarefree_radicalproof · cited by 0