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On a Theorem on Ordered Groups
Published online by Cambridge University Press: 18 May 2009
Extract
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.
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- Copyright © Glasgow Mathematical Journal Trust 1958
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