Theorems · Definition · commutative algebra
normalize
{α : Type u_1} → [inst : MonoidWithZero α] → [NormalizationMonoid α] → α → αChooses an element of each associate class, by multiplying by normUnit
- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 137 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 41 definitions · uses no axioms
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.
- Units.valproof · cited by 1,966
- MonoidWithZerostatement and proof · cited by 456
- NormalizationMonoidstatement and proof · cited by 165
- NormalizationMonoid.normUnitproof · cited by 33
Cited by155
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactorsproof · cited by 151
- normalize_eqstatement · cited by 26
- UniqueFactorizationMonoid.prime_of_normalized_factorproof · cited by 23
- UniqueFactorizationMonoid.prod_normalizedFactorsproof · cited by 23
- normalize_zerostatement · cited by 16
- dvd_antisymm_of_normalize_eqstatement and proof · cited by 15
- Associates.outproof · cited by 15
- UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactorsstatement and proof · cited by 14
- UniqueFactorizationMonoid.normalizedFactors_zeroproof · cited by 14
- Polynomial.map_dvd_map'proof · cited by 14
- normalize_gcdstatement · cited by 13
- UniqueFactorizationMonoid.normalizedFactors_mulproof · cited by 11