Approximation properties for orderings on \({}^*\)-fields. (English) Zbl 0706.12005
Summary: The goal of this paper is to extend the main theorems on approximation properties of the topological space of orderings from formally real fields to skew fields with an involution \({}^*\). To accomplish this the concept of \({}^*\)-semiordering is developed and new theorems are obtained for lifting \({}^*\)-orderings from the residue class field of a real valuation.
MSC:
12J15 | Ordered fields |
16K40 | Infinite-dimensional and general division rings |
12E15 | Skew fields, division rings |
16W10 | Rings with involution; Lie, Jordan and other nonassociative structures |
12D15 | Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) |