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On ordered division rings

Tom 88 / 2001

Colloquium Mathematicum 88 (2001), 263-271 MSC: Primary 06F25, 16W10. DOI: 10.4064/cm88-2-8

Streszczenie

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 $x\mapsto xa^2$ for non-zero $a$, in place of requiring that positive elements have a positive product. Our aim in this work is to study this type of ordering in the case of a division ring. We show that it actually behaves just as in the commutative case. Further, we show that the bounded subring associated with that ordering is a valuation ring which is preserved under conjugation, so one can associate with the semiordering a natural valuation.

Autorzy

• Ismail M. IdrisDepartment of Mathematics
Faculty of Science
Ain-Shams University
Cairo, Egypt
e-mail

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