Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.exists_mem_normalizedFactors
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
{x : α}, x ≠ 0 → ¬IsUnit x → ∃ p, p ∈ UniqueFactorizationMonoid.normalizedFactors x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- IsUnitstatement and proof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Irreducibleproof · 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
- WfDvdMonoid.exists_irreducible_factorproof · cited by 12
- UniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvdproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_posproof · cited by 1
- Polynomial.irreducible_of_dvd_cyclotomic_of_natDegreeproof · cited by 1