Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.irreducible_of_factor
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a : α},
∀ x ∈ UniqueFactorizationMonoid.factors a, Irreducible x- Cited by
- 13 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
- Irreduciblestatement · cited by 496
- UniqueFactorizationMonoidstatement and proof · cited by 279
- UniqueFactorizationMonoid.factorsstatement and proof · cited by 55
- Prime.irreducibleproof · cited by 54
- UniqueFactorizationMonoid.prime_of_factorproof · cited by 9
Cited by14
Results whose statement or proof uses this declaration.
- Associates.factors'proof · cited by 15
- IsAlgClosed.of_exists_rootproof · cited by 5
- UniqueFactorizationMonoid.exists_mem_factors_of_dvdproof · cited by 4
- Associates.map_subtype_coe_factors'proof · cited by 3
- UniqueFactorizationMonoid.card_factors_of_irreducibleproof · cited by 2
- UniqueFactorizationMonoid.factors_oneproof · cited by 2
- UniqueFactorizationMonoid.factors_rel_of_associatedproof · cited by 2
- UniqueFactorizationMonoid.factors_mulproof · cited by 1
- perfectField_iff_splits_of_natSepDegree_eq_oneproof · cited by 1
- IsSepClosed.of_exists_rootproof · cited by 1
- Associated.card_factors_eqproof · cited by 1
- Polynomial.splits_iff_splitsproof · cited by 0