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Title: On ordered division rings (English)
Author: Idris, Ismail M.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 1
Year: 2003
Pages: 69-76
Summary lang: English
Category: math
Summary: 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 $x \rightarrow x a^2$ 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. (English)
Keyword: ordering
Keyword: division ring
MSC: 06F25
MSC: 12E15
MSC: 16K40
MSC: 16W10
MSC: 16W80
idZBL: Zbl 1014.06017
idMR: MR1961999
Date available: 2009-09-24T10:59:07Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] A.  Prestel: Lectures on Formally Real Fields. Lecture Notes in Math. 1093.Springer Verlag, , 1984. MR 0769847
Reference: [2] T. Szele: On ordered skew fields.Proc. Amer. Math. Soc. 3 (1952), 410–413. Zbl 0047.03104, MR 0047017, 10.1090/S0002-9939-1952-0047017-7


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