Theorems · Theorem · group theory
Irreducible.isRelPrime_iff_not_dvd
∀ {M : Type u_1} [inst : Monoid M] {p n : M}, Irreducible p → (IsRelPrime p n ↔ ¬p ∣ n)See also Irreducible.coprime_iff_not_dvd.
- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- IsUnitproof · cited by 1,602
- Irreduciblestatement and proof · cited by 496
- Associatedproof · cited by 296
- Dvd.dvd.transproof · cited by 148
- IsRelPrimestatement and proof · cited by 136
- dvd_rflproof · cited by 80
- Irreducible.not_isUnitproof · cited by 42
- Associated.dvdproof · cited by 38
- Irreducible.dvd_iffproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Irreducible.coprime_iff_not_dvdproof · cited by 5
- UniqueFactorizationMonoid.pairwise_primeFactors_isRelPrimeproof · cited by 1
- Irreducible.dvd_or_isRelPrimeproof · cited by 1
- exists_squarefree_dvd_pow_of_ne_zeroproof · cited by 1