Theorems · Definition · commutative algebra
NormalizationMonoid.normUnit
{α : Type u_2} → {inst : MonoidWithZero α} → [self : NormalizationMonoid α] → α → αˣnormUnit assigns to each element of the monoid a unit of the monoid.
- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- NormalizationMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement · cited by 2,804
- MonoidWithZerostatement and proof · cited by 456
- NormalizationMonoidstatement and proof · cited by 165
Cited by39
Results whose statement or proof uses this declaration.
- normalizeproof · cited by 137
- Polynomial.map_dvd_map'proof · cited by 14
- associated_normalizeproof · cited by 11
- normalize_eq_oneproof · cited by 10
- normalize_applystatement · cited by 8
- Polynomial.coe_normUnitstatement and proof · cited by 7
- normalize_eq_normalize_iff_associatedproof · cited by 5
- normalize_idemproof · cited by 4
- normalize_mulproof · cited by 4
- NormalizationMonoid.normUnit_onestatement · cited by 4
- CommGroupWithZero.coe_normUnitstatement · cited by 3
- NormalizationMonoid.normUnit_mul_unitsstatement · cited by 3