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Construction of orders in Abelian groups

Published online by Cambridge University Press:  24 October 2008

H.-H. Teh
H.-H. Teh
Affiliation:
Queen's UniversityBelfast
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 476 - 482
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

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