Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.prime_of_factor
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : UniqueFactorizationMonoid α] {a : α},
∀ x ∈ UniqueFactorizationMonoid.factors a, Prime x- Cited by
- 9 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Primestatement · cited by 277
- UniqueFactorizationMonoid.factorsstatement and proof · cited by 55
- UniqueFactorizationMonoid.exists_prime_factorsproof · cited by 6
- UniqueFactorizationMonoid.ne_zero_of_mem_factorsproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.irreducible_of_factorproof · cited by 13
- Ideal.IsPrime.exists_mem_prime_of_ne_botproof · cited by 3
- Ideal.IsDedekindDomain.ramificationIdx_eq_factors_countproof · cited by 2
- Ideal.Factors.ne_botproof · cited by 1
- Submodule.isInternal_prime_power_torsion_of_is_torsion_by_idealproof · cited by 1
- Submodule.exists_isInternal_prime_power_torsion_of_pidproof · cited by 1
- Submonoid.LocalizationMap.uniqueFactorizationMonoidproof · cited by 1
- Ideal.factors_span_eqproof · cited by 0
- Submodule.exists_isInternal_prime_power_torsionproof · cited by 0