= Hahn group
{c}
{title2=$V(\Gamma,\mathbb R)$}
For a <totally ordered set> $\Gamma$, take real coefficient families whose support satisfies the maximum condition: every nonempty subset of the support has a largest index. Add coefficients pointwise and decide the sign from the largest nonzero coordinate. This defines an ordered <Abelian group>. For $\Gamma=\mathbb Z_{>0}$ with its usual order, the maximum condition forces finite support. Some presentations reverse the index order and use a minimum instead; specify the convention when applying an embedding theorem.
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