Theorems · Theorem · group theory
associated_iff_eq
∀ {M : Type u_1} [inst : Monoid M] [Subsingleton Mˣ] {x y : M}, Associated x y ↔ x = y- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
- Assumes
- MonoidSubsingleton
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.
- Monoidstatement and proof · cited by 3,887
- mul_oneproof · cited by 3,885
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- Associatedstatement · cited by 296
- Units.eq_oneproof · cited by 3
Cited by28
Results whose statement or proof uses this declaration.
- associated_eq_eqproof · cited by 6
- Ideal.finprod_heightOneSpectrum_factorizationproof · cited by 6
- eq_of_prime_pow_eqproof · cited by 5
- Ideal.prod_normalizedFactors_eq_selfproof · cited by 4
- Ideal.IsDedekindDomain.ramificationIdx'_ne_zeroproof · cited by 3
- DivisorChain.eq_pow_second_of_chain_of_has_chainproof · cited by 2
- FractionalIdeal.count_maximal_coprimeproof · cited by 2
- Int.associated_iff_natAbsproof · cited by 2
- Ideal.finprod_not_dvdproof · cited by 1
- DivisorChain.element_of_chain_eq_pow_second_of_chainproof · cited by 1
- Submodule.isInternal_prime_power_torsion_of_is_torsion_by_idealproof · cited by 1
- DivisorChain.exists_chain_of_prime_powproof · cited by 1