Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.factors_prod
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a : α},
a ≠ 0 → Associated (UniqueFactorizationMonoid.factors a).prod a- Cited by
- 18 results in Mathlib
- Foundations
- Depth 21 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.
- Multisetproof · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.prodstatement and proof · cited by 528
- Associatedstatement and proof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- UniqueFactorizationMonoid.factorsstatement · cited by 55
- UniqueFactorizationMonoid.exists_prime_factorsproof · cited by 6
Cited by18
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.dvd_of_mem_factorsproof · cited by 5
- IsAlgClosed.of_exists_rootproof · cited by 5
- UniqueFactorizationMonoid.exists_mem_factors_of_dvdproof · cited by 4
- Ideal.IsPrime.exists_mem_prime_of_ne_botproof · cited by 3
- UniqueFactorizationMonoid.factors_oneproof · cited by 2
- UniqueFactorizationMonoid.factors_rel_of_associatedproof · cited by 2
- UniqueFactorizationMonoid.card_factors_of_irreducibleproof · cited by 2
- UniqueFactorizationMonoid.factors_mulproof · cited by 1
- Submodule.isInternal_prime_power_torsion_of_is_torsion_by_idealproof · cited by 1
- perfectField_iff_splits_of_natSepDegree_eq_oneproof · cited by 1
- Submonoid.LocalizationMap.uniqueFactorizationMonoidproof · cited by 1
- IsSepClosed.of_exists_rootproof · cited by 1