Theorems · Theorem · commutative algebra
NormalizationMonoid.normUnit_mul_units
∀ {α : Type u_2} {inst : MonoidWithZero α} [self : NormalizationMonoid α] {a : α} (u : αˣ),
a ≠ 0 → normUnit (a * ↑u) = u⁻¹ * normUnit aThe condition that ensures associated elements are normalized to the same element.
- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- NormalizationMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement · cited by 2,804
- Units.valstatement · cited by 1,966
- MonoidWithZerostatement and proof · cited by 456
- NormalizationMonoidstatement and proof · cited by 165
- NormalizationMonoid.normUnitstatement · cited by 33
Cited by3
Results whose statement or proof uses this declaration.
- normalize_eq_normalize_iff_associatedproof · cited by 5
- normUnit_coe_unitsproof · cited by 1
- normUnit_mul_normUnitproof · cited by 1