Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.primeFactors_zero
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [inst_1 : NormalizationMonoid M] [inst_2 : UniqueFactorizationMonoid M],
UniqueFactorizationMonoid.primeFactors 0 = ∅- Defined in
- Mathlib.RingTheory.Radical.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 74 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.
- Finsetstatement · cited by 13,712
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Multiset.toFinsetproof · cited by 230
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.primeFactorsstatement · cited by 32
- UniqueFactorizationMonoid.normalizedFactors_zeroproof · cited by 14
Cited by4
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.radical_zeroproof · cited by 7
- UniqueFactorizationMonoid.primeFactors_eq_primeFactors_natAbsproof · cited by 1
- UniqueFactorizationMonoid.primeFactors_mul_eq_disjUnionproof · cited by 1
- UniqueFactorizationMonoid.pairwise_primeFactors_isRelPrimeproof · cited by 1