Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.normalizedFactors_irreducible
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
{a : α}, Irreducible a → UniqueFactorizationMonoid.normalizedFactors a = {normalize a}- Cited by
- 10 results in Mathlib
- Foundations
- Depth 26 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.
- Multisetstatement and proof · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement and proof · cited by 496
- Associatedproof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- normalizestatement and proof · cited by 137
- Irreducible.ne_zeroproof · cited by 45
- UniqueFactorizationMonoid.prime_of_normalized_factorproof · cited by 23
- UniqueFactorizationMonoid.prod_normalizedFactorsproof · cited by 23
- UniqueFactorizationMonoid.normalize_normalized_factorproof · cited by 9
Cited by10
Results whose statement or proof uses this declaration.
- Ideal.IsDedekindDomain.ramificationIdx'_eq_normalizedFactors_countproof · cited by 5
- UniqueFactorizationMonoid.normalizedFactors_of_irreducible_powproof · cited by 2
- UniqueFactorizationMonoid.radical_of_primeproof · cited by 1
- Ideal.eq_prime_pow_of_succ_lt_of_leproof · cited by 1
- IsLocalization.OverPrime.mem_normalizedFactors_of_isPrimeproof · cited by 1
- UniqueFactorizationMonoid.normalizedFactors_prod_eqproof · cited by 0
- Irreducible.normalizedFactors_powproof · cited by 0
- KummerDedekind.Ideal.irreducible_map_of_irreducible_minpolyproof · cited by 0
- Ideal.eq_span_singleton_of_mem_of_notMem_sq_of_notMem_prime_neproof · cited by 0