Characterization of fans in *-fields (Q921059)

Let D be a skew field with involution *. Then the notions of *-orderings, (real) *-valuations and compatibility are defined extending the commutative theory. This paper contains two main results. The first one (Theorem 2.5) describes the set \(X^ v_ T\) of *-orderings containing a preordering T and compatible with a real *-valuation v in terms of the set \(X_{\bar T}\) of the residue field and the character group of the ``symmetric'' value group reduced by v(T). (This extends the classical result of Baer and Krull into the setting of *-fields.) Then the author turns his attention to fans - a special type of preorderings which allow for a ``maximal number'' of extensions to orderings. He transfers results proved by Bröcker for commutative fields into the context of *-fields, especially a valuation theoretic characterization of fans (Theorem 2.13).