Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.normalizedFactors_one
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α],
UniqueFactorizationMonoid.normalizedFactors 1 = 0- Cited by
- 8 results in Mathlib
- Foundations
- Depth 27 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.
- Multisetstatement · cited by 2,627
- Nontrivialproof · cited by 2,416
- CommMonoidWithZerostatement and proof · cited by 913
- one_ne_zeroproof · cited by 885
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Multiset.map_congrproof · cited by 232
- NormalizationMonoidstatement and proof · cited by 165
- subsingleton_or_nontrivialproof · cited by 161
- UniqueFactorizationMonoid.normalizedFactorsstatement · cited by 151
- normalizeproof · cited by 137
- UniqueFactorizationMonoid.prod_normalizedFactorsproof · cited by 23
- Multiset.notMem_zeroproof · cited by 17
Cited by8
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_powproof · cited by 8
- UniqueFactorizationMonoid.primeFactors_radicalproof · cited by 5
- UniqueFactorizationMonoid.normalizedFactors_prod_of_primeproof · cited by 2
- Ideal.IsDedekindDomain.emultiplicity_map_eq_ramificationIdx'_mulproof · cited by 2
- UniqueFactorizationMonoid.primeFactors_oneproof · cited by 2
- UniqueFactorizationMonoid.normalizedFactors_prod_eqproof · cited by 0
- factorization_oneproof · cited by 0
- UniqueFactorizationMonoid.normalizedFactors_multiset_prodproof · cited by 0