关于有序域的几则短记

Some Remarks on Ordered Fields

中文摘要:

      

英文摘要:

      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.