On Ordered Division Rings |
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Authors: | Ismail M Idris |
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Institution: | (1) Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt |
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Abstract: | Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel's axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under x xa
2 for nonzero a, instead of requiring that positive elements have a positive product. In this work, this type of ordering is studied in the case of a division ring. It is shown that it actually behaves the same as in the commutative case. Further, it is shown that the bounded subring associated with that ordering is a valuation ring which is preserved under conjugation, so one can associate a natural valuation to a semiordering. |
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Keywords: | ordering division ring |
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