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On ordered division rings

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Idris I.

Colloquium Mathematicum

2001

tom 88

nr 2

263-271

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 ↦ xa² 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.

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1 Colloquium Mathematicum

1 Idris I.

1 2001

Wyniki wyszukiwania

On ordered division rings