Theorems · Theorem · commutative algebra
Irreducible.dvd_iff_not_isCoprime
∀ {R : Type u} [inst : CommRing R] [IsBezout R] {p n : R}, Irreducible p → (p ∣ n ↔ ¬IsCoprime p n)See also Irreducible.coprime_iff_not_dvd'.
- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Irreduciblestatement and proof · cited by 496
- IsCoprimestatement · cited by 321
- IsBezoutstatement and proof · cited by 23
- iff_not_commproof · cited by 16
- Irreducible.coprime_iff_not_dvdproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Irreducible.isCoprime_or_dvdproof · cited by 1