Wefelscheid (Untersuchungen über Fastkörper und Fastbereiche, Habilitationsschrift, Hamburg, 1971) generalised the well-known Theorem of Artin/Schreier about the characterization of formally real fields and the fundamental result of Baer/Krull to near-fields. In the last fifty years arose from the Theorem of Baer/Krull a theory, which analyses the entirety of the orderings of a field (E. Becker, L. Bröcker, M. Marshall et al.), as presented e.g. in the book by Lam (Orderings, valuations and quadratic forms, American Mathematical Society, Providence, 1983). At the centre of this theory are preorders and their compatibility with valuations or places. We develop some essential results of this theory for the near-field case. In particular, we derive the Brown/Marshall’s inequalities and Bröcker’s Theorem on the trivialisation of fans in the near-field case.

Wefelscheid (Untersuchungen über Fastkörper und Fastbereiche, Habilitationsschrift, Hamburg, 1971) 概括了著名的Artin/Schreier 定理关于形式实场的表征和Baer/Krull 对近场的基本结果。在过去的 50 年里，Baer/Krull 定理产生了一个理论，它分析了一个域的整个排序（E. Becker、L. Bröcker、M. Marshall 等人），例如在书中提出的Lam（排序、估值和二次形式，美国数学学会，普罗维登斯，1983 年）。该理论的核心是预订及其与估值或地点的兼容性。我们针对近场情况开发了该理论的一些基本结果。特别是，