Title:

On ordered division rings (English) 
Author:

Idris, Ismail M. 
Language:

English 
Journal:

Czechoslovak Mathematical Journal 
ISSN:

00114642 (print) 
ISSN:

15729141 (online) 
Volume:

53 
Issue:

1 
Year:

2003 
Pages:

6976 
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 (ArtinSchreier) 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:

20090924T10:59:07Z 
Last updated:

20200703 
Stable URL:

http://hdl.handle.net/10338.dmlcz/127781 
. 
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/S00029939195200470177 
. 