Theorems · Definition · commutative algebra

NormalizationMonoid.ofRightInverse

{α : Type u_2} →
  [inst : MonoidWithZero α] →
    [IsLeftCancelMulZero α] →
      (out : Associates α → α) → (∀ (a : Associates α), Associates.mk (out a) = a) → out 1 = 1 → NormalizationMonoid α

Construct a NormalizationMonoid from a right inverse of Associates.mk.

Defined in: Mathlib.Algebra.GCDMonoid.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MonoidWithZero IsLeftCancelMulZero

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Unitsproof · cited by 2,804
MonoidWithZerostatement and proof · cited by 456
Associatedproof · cited by 296
Associatesstatement and proof · cited by 210
NormalizationMonoidstatement · cited by 165
Associates.mkstatement and proof · cited by 137
IsLeftCancelMulZerostatement and proof · cited by 48
Classical.decproof · cited by 10

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.