orderMonoidWithZeroEquiv — Mathlib

English

In the setting of a linearly ordered group with zero, there is a bijective correspondence between the unit group and the integers via an isomorphism to ℤᵐ⁰.

Русский

Существуют изоморфизмы между нулём устройства и целыми через единичную группу и ℤᵐ⁰.

LaTeX

$$orderMonoidWithZeroEquiv G$$

Lean4

/-- Any nontrivial linearly ordered abelian group with zero that is locally finite
is isomorphic to `ℤᵐ⁰`. -/
noncomputable def orderMonoidWithZeroEquiv (G : Type*) [LinearOrderedCommGroupWithZero G] [LocallyFiniteOrder Gˣ]
    [Nontrivial Gˣ] : G ≃*o ℤᵐ⁰ :=
  OrderMonoidIso.withZeroUnits.symm.trans (LocallyFiniteOrder.orderMonoidEquiv _).withZero

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