Theorems · Theorem · group theory
Associates.mk_eq_mk_iff_associated
∀ {M : Type u_1} [inst : Monoid M] {a b : M}, Associates.mk a = Associates.mk b ↔ Associated a b- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Associatedstatement · cited by 296
- Associatesstatement · cited by 210
- Associates.mkstatement · cited by 137
Cited by16
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.prod_normalizedFactorsproof · cited by 23
- Ideal.finprod_heightOneSpectrum_factorizationproof · cited by 6
- IsDiscreteValuationRing.associated_pow_irreducibleproof · cited by 4
- Associates.unique'proof · cited by 2
- Associates.mem_factors'_of_dvdproof · cited by 2
- FractionalIdeal.count_maximal_coprimeproof · cited by 2
- Associates.mk_normalizeproof · cited by 2
- Ideal.torsionOf_eq_span_pow_pOrderproof · cited by 2
- Associates.mk_injectiveproof · cited by 1
- IsDiscreteValuationRing.addVal_eq_iff_associatedproof · cited by 0
- Associates.mk_eq_oneproof · cited by 0