Theorems · Theorem · group theory
Irreducible.dvd_irreducible_iff_associated
∀ {M : Type u_1} [inst : Monoid M] {p q : M}, Irreducible p → Irreducible q → (p ∣ q ↔ Associated p q)- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Irreduciblestatement and proof · cited by 496
- Associatedstatement · cited by 296
- Associated.dvdproof · cited by 38
- Irreducible.associated_of_dvdproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Prime.dvd_prime_iff_associatedproof · cited by 3
- emultiplicity_eq_zero_of_irreducible_neproof · cited by 0