Construction of orders in Abelian groups

Let G be an Abelian group. A binary relation ≥ denned in G is called an order of G if for each x, y, z e 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 .