| 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:
|
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/S0002-9939-1952-0047017-7 |
| . |
