# On ordered division rings

Czechoslovak Mathematical Journal (2003)

- Volume: 53, Issue: 1, page 69-76
- ISSN: 0011-4642

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topIdris, Ismail M.. "On ordered division rings." Czechoslovak Mathematical Journal 53.1 (2003): 69-76. <http://eudml.org/doc/30759>.

@article{Idris2003,

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 $x \rightarrow x a^2$ 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.},

author = {Idris, Ismail M.},

journal = {Czechoslovak Mathematical Journal},

keywords = {ordering; division ring; ordering; division ring},

language = {eng},

number = {1},

pages = {69-76},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On ordered division rings},

url = {http://eudml.org/doc/30759},

volume = {53},

year = {2003},

}

TY - JOUR

AU - Idris, Ismail M.

TI - On ordered division rings

JO - Czechoslovak Mathematical Journal

PY - 2003

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 53

IS - 1

SP - 69

EP - 76

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 $x \rightarrow x a^2$ 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.

LA - eng

KW - ordering; division ring; ordering; division ring

UR - http://eudml.org/doc/30759

ER -

## References

top- Lectures on Formally Real Fields. Lecture Notes in Math. 1093, Springer Verlag, , 1984. (1984) MR0769847
- 10.1090/S0002-9939-1952-0047017-7, Proc. Amer. Math. Soc. 3 (1952), 410–413. (1952) Zbl0047.03104MR0047017DOI10.1090/S0002-9939-1952-0047017-7

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