Theorems · Definition · commutative algebra
Associates.out
{α : Type u_1} → [inst : MonoidWithZero α] → [NormalizationMonoid α] → Associates α → αMaps an element of Associates back to the normalized element of its associate class
- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- MonoidWithZerostatement and proof · cited by 456
- Associatesstatement · cited by 210
- NormalizationMonoidstatement and proof · cited by 165
- normalizeproof · cited by 137
Cited by17
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_mulproof · cited by 11
- associatesEquivOfUniqueUnitsproof · cited by 7
- associatesEquivOfUniqueUnits_applystatement · cited by 2
- Associated.normalizedFactors_eqproof · cited by 2
- Associates.out_mkstatement · cited by 2
- Associates.mk_outstatement · cited by 1
- associatesIntEquivNatproof · cited by 0
- Associates.normalize_outstatement · cited by 0
- Associates.out_dvd_iffstatement · cited by 0
- Associates.out_eq_zero_iffstatement · cited by 0
- Associates.out_injectivestatement · cited by 0
- Associates.out_mulstatement · cited by 0