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