Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.radical_of_prime
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M]
{a : M}, Prime a → UniqueFactorizationMonoid.radical a = normalize a- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Multisetproof · cited by 2,627
- Finset.prodproof · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- Finset.prod_congrproof · cited by 646
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Primestatement and proof · cited by 277
- Multiset.toFinsetproof · cited by 230
- NormalizationMonoidstatement and proof · cited by 165
- normalizestatement and proof · cited by 137
- Finset.prod_singletonproof · cited by 78
- UniqueFactorizationMonoid.radicalstatement · cited by 64
Cited by1
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.radical_pow_of_primeproof · cited by 1