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On a Theorem on Ordered Groups

Published online by Cambridge University Press:  18 May 2009

C. G. Chehata
C. G. Chehata
Affiliation:
Faculty of Science, The University Alexandria
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The following work establishes a new proof of the theorem: Every archimedean ordered group is abelian. This theorem has been proved differently by many authors. It was first proved by O. Hölder [2]. A second proof has been given by H. Cartan [1]: he uses the topology which is naturally introduced in the group by its order.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 1 , December 1958 , pp. 16 - 21
Copyright
Copyright © Glasgow Mathematical Journal Trust 1958

References

1.Cartan, H., Un théorème sur les groupes ordonnès, Bull. Sci. Math., 63 (1939), 201–205.Google Scholar
2.Hölder, O., Die Axiome der Quantitat and die Lehre von Mass, Ber. Verh. Säclis. Ges. Wisa. Leipzig Math.-Phys. Cl., 53 (1901), 1–64.Google Scholar
3.Levi, F. W., Ordered groups, Proc. Indian Acad. Sci., 16 (1942), 256–263.CrossRefGoogle Scholar
4.Levi, F. W., Contributions to the theory of ordered groups, Proc. Indian Acad. Sci., 17 (1943), 199–201.CrossRefGoogle Scholar