Theorems · Definition · order theory
LocallyFiniteOrder.orderMonoidWithZeroHom
(G : Type u_3) → [inst : LinearOrderedCommGroupWithZero G] → [LocallyFiniteOrder Gˣ] → G →*₀o WithZero (Multiplicative ℤ)
Any linearly ordered abelian group with zero that is locally finite embeds into ℤᵐ⁰.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement and proof · cited by 2,804
- Multiplicativestatement and proof · cited by 875
- MonoidWithZeroHomproof · cited by 704
- LocallyFiniteOrderstatement and proof · cited by 658
- WithZerostatement and proof · cited by 586
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidHomClass.toMonoidHomproof · cited by 294
- OrderMonoidWithZeroHomstatement · cited by 48
- WithZero.map'proof · cited by 45
- OrderMonoidIso.symmproof · cited by 44
- MonoidWithZeroHom.compproof · cited by 34
- OrderMonoidIso.toMulEquivproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- LocallyFiniteOrder.orderMonoidWithZeroHom_strictMonostatement · cited by 0