| 戴执中.关于有序域的几则短记[J].数学研究及应用,1982,2(2):7~10 |
| 关于有序域的几则短记 |
| Some Remarks on Ordered Fields |
| 投稿时间：1981-05-20 |
| DOI：10.3770/j.issn:2095-2651.1982.02.002 |
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| In this note, Dubois' counter-example to Lang's formulation of Hilbert's 17-th problem is re-examined, besides, a field admitting only one ordering is constructed which has a non-henselian valuation ring compatible with its ordering. Let F=Q(?), let t be an indeterminate, let F(t) be ordered so that t is posi tive and infinitesimal, and let K be the quadratic closure of F(t) with respect to the given ordering. The canonical valuation ring A of K is of course compatible with the unique ordering of K. However, it is shown that A is not henselian. |
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