Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.dvd_of_mem_factors
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {p a : α},
p ∈ UniqueFactorizationMonoid.factors a → p ∣ a- Cited by
- 5 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- UniqueFactorizationMonoid.factorsstatement and proof · cited by 55
- dvd_transproof · cited by 50
- Associated.dvdproof · cited by 38
- UniqueFactorizationMonoid.factors_prodproof · cited by 18
- Multiset.dvd_prodproof · cited by 7
- UniqueFactorizationMonoid.ne_zero_of_mem_factorsproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.uniqueFactorizationMonoidproof · cited by 1
- IsSepClosed.of_exists_rootproof · cited by 1
- perfectField_iff_splits_of_natSepDegree_eq_oneproof · cited by 1
- Polynomial.splits_iff_splitsproof · cited by 0
- Ideal.Factors.ramificationIdx_ne_zeroproof · cited by 0