Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.zero_notMem_normalizedFactors
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
(x : α), 0 ∉ UniqueFactorizationMonoid.normalizedFactors x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 23 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.
- Multisetstatement · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- Prime.ne_zeroproof · cited by 47
- UniqueFactorizationMonoid.prime_of_normalized_factorproof · cited by 23
Cited by5
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.radical_ne_zeroproof · cited by 5
- Polynomial.mem_normalizedFactors_iffproof · cited by 2
- UniqueFactorizationMonoid.ne_zero_of_mem_normalizedFactorsproof · cited by 1
- UniqueFactorizationMonoid.count_normalizedFactors_eq'proof · cited by 1
- Polynomial.normalizedFactors_cyclotomic_cardproof · cited by 0