Geodesic
On ordered division rings
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 69-76.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 06F25, 12E15, 16K40, 16W10, 16W80
Keywords: ordering; division ring 
@article{CMJ_2003__53_1_a5,
     author = {Idris, Ismail M.},
     title = {On ordered division rings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {69--76},
     publisher = {mathdoc},
     volume = {53},
     number = {1},
     year = {2003},
     mrnumber = {1961999},
     zbl = {1014.06017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2003__53_1_a5/}
}
TY  - JOUR
AU  - Idris, Ismail M.
TI  - On ordered division rings
JO  - Czechoslovak Mathematical Journal
PY  - 2003
SP  - 69
EP  - 76
VL  - 53
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2003__53_1_a5/
LA  - en
ID  - CMJ_2003__53_1_a5
ER  - 
%0 Journal Article
%A Idris, Ismail M.
%T On ordered division rings
%J Czechoslovak Mathematical Journal
%D 2003
%P 69-76
%V 53
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2003__53_1_a5/
%G en
%F CMJ_2003__53_1_a5
Idris, Ismail M. On ordered division rings. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 69-76. http://geodesic.mathdoc.fr/item/CMJ_2003__53_1_a5/