Theorems · Theorem · group theory
Associates.irreducible_mk
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {a : M}, Irreducible (Associates.mk a) ↔ Irreducible a- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- IsUnitproof · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- Irreduciblestatement · cited by 496
- Associatedproof · cited by 296
- Associatesstatement and proof · cited by 210
- Associates.mkstatement and proof · cited by 137
- Iff.andproof · cited by 33
- Associated.reflproof · cited by 25
- Associated.commproof · cited by 7
Cited by11
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.associates_irreducibleproof · cited by 11
- Ideal.finprod_heightOneSpectrum_factorizationproof · cited by 6
- Associates.count_ne_zero_iff_dvdproof · cited by 5
- FractionalIdeal.count_well_definedproof · cited by 5
- IsDedekindDomain.HeightOneSpectrum.maxPowDividing_eq_pow_multiset_countproof · cited by 2
- Associates.unique'proof · cited by 2
- Associates.mem_factors'_of_dvdstatement · cited by 2
- Ideal.torsionOf_eq_span_pow_pOrderproof · cited by 2
- Associates.exists_prime_dvd_of_not_inf_oneproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_oneproof · cited by 1
- Associates.mem_factors'_iff_dvdstatement and proof · cited by 0