Theorems · Definition · commutative algebra
associatesEquivOfUniqueUnits
{α : Type u_1} → [inst : CommMonoidWithZero α] → [Subsingleton αˣ] → Associates α ≃* αIf a monoid's only unit is 1, then it is isomorphic to its associates.
- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Unitsstatement and proof · cited by 2,804
- MulEquivstatement · cited by 1,142
- CommMonoidWithZerostatement and proof · cited by 913
- Associatesstatement · cited by 210
- Associates.mkproof · cited by 137
- Associates.outproof · cited by 15
Cited by8
Results whose statement or proof uses this declaration.
- mkFactorOrderIsoOfFactorDvdEquivproof · cited by 4
- associatesEquivOfUniqueUnits_applystatement and proof · cited by 2
- associatesEquivOfUniqueUnits_symm_applystatement and proof · cited by 2
- mkFactorOrderIsoOfFactorDvdEquiv_apply_coestatement · cited by 2
- emultiplicity_factor_dvd_iso_eq_emultiplicity_of_mem_normalizedFactorsproof · cited by 1
- mem_normalizedFactors_factor_dvd_iso_of_mem_normalizedFactorsproof · cited by 1
- associatesEquivOfUniqueUnits.congr_simpstatement and proof · cited by 0
- mkFactorOrderIsoOfFactorDvdEquiv_symm_apply_coestatement · cited by 0