M. Mahdavi-Hezavehi: Characterizing the Multiplicative Group of a Real Closed Field in terms of its Divisible Maximal Subgroup


Submission: 2008, Sep 10

Let $ F $ be a field and $ M $ be a maximal subgroup of the multiplicative group $ F^* = F \setminus \{0\} $. It is proved that if $ M $ is divisible, then $ F $ is Euclidean. Furthermore, it is shown that $ F^* $ contains a divisible maximal subgroup if and only if $ F^* $ is isomorphic to the multiplicative group of a real closed field.

2000 Mathematics Subject Classification:

Keywords and Phrases:

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