Places of Near-Fields: To Heinrich Wefelscheid

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