Construction of orders in Abelian groups
Hoon Heng Teh · Mathematical Proceedings of the Cambridge Philosophical Society · 1961
Let G be an Abelian group. A binary relation ≥ denned in G is called an order of G if for each x, y, z ε G, (i) x ≥ y or y ≥ x (and hence x ≥ x); (ii) x ≥ y and y ≥ x ⇒ x = y, (if x ≥ y and x ≠ y, we write x > y); (iii) x ≥ y and y ≥ z ⇒ x = z; (iv) z ≥ y ⇒ x + z ≥ y + z.