Theorems · Theorem · group theory
Prime.dvd_prime_iff_associated
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {p q : M},
Prime p → Prime q → (p ∣ q ↔ Associated p q)- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
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.
- CommMonoidWithZerostatement and proof · cited by 913
- Associatedstatement · cited by 296
- Primestatement and proof · cited by 277
- IsCancelMulZerostatement and proof · cited by 177
- Prime.irreducibleproof · cited by 54
- Irreducible.dvd_irreducible_iff_associatedproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- prime_dvd_prime_iff_eqproof · cited by 2
- Associated.of_pow_associated_of_primeproof · cited by 2
- Ideal.finprod_not_dvdproof · cited by 1