On ordered division rings

Ismail M. Idris. "On ordered division rings." Colloquium Mathematicae 88.2 (2001): 263-271. <http://eudml.org/doc/283838>.

@article{IsmailM2001,
abstract = {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.},
author = {Ismail M. Idris},
journal = {Colloquium Mathematicae},
keywords = {ordered division rings; Prestel semiorder; semiordered division ring; valuations},
language = {eng},
number = {2},
pages = {263-271},
title = {On ordered division rings},
url = {http://eudml.org/doc/283838},
volume = {88},
year = {2001},
}

TY - JOUR
AU - Ismail M. Idris
TI - On ordered division rings
JO - Colloquium Mathematicae
PY - 2001
VL - 88
IS - 2
SP - 263
EP - 271
AB - 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.
LA - eng
KW - ordered division rings; Prestel semiorder; semiordered division ring; valuations
UR - http://eudml.org/doc/283838
ER -