Theorems · Theorem · group theory
Associated.dvd_iff_dvd_left
∀ {M : Type u_1} [inst : Monoid M] {a b c : M}, Associated a b → (a ∣ c ↔ b ∣ c)- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- 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
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- Associatedstatement and proof · cited by 296
- Units.mul_right_dvdproof · cited by 7
Cited by6
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactorsproof · cited by 11
- lcm_dvd_iffproof · cited by 6
- Polynomial.exists_monic_irreducible_factorproof · cited by 3
- IsIntegrallyClosed.eq_map_mul_C_of_dvdproof · cited by 2
- irreducible_iff_prime_of_existsUnique_irreducible_factorsproof · cited by 1
- IsCyclotomicExtension.Rat.zeta_sub_one_dvd_intCast_iffproof · cited by 1