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Tytuł artykułu

On ordered division rings

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Abstrakty

EN
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.

Twórcy

  • Department of Mathematics, Faculty of Science, Ain-Shams University, Cairo, Egypt

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bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-2-8