Quasi-ordered fields (Q1093681)

The author calls a field with a binary relation \(\leq\) ``quasi-ordered'' if a set of axioms closely related to the axioms of ordered fields is fulfilled. Every ordered field is quasi-ordered, and on every Krull valued field a quasi-order is induced by the valuation, so this definition is a common generalization of both orderings and valuations. On the other hand these are the only possible types of quasi-ordered fields, since the main theorem says that every such field either is an ordered field or a Krull valued field whose valuation induces the given quasi-order.