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Igor Klep; Dejan Velušček
The Joly–Becker theorem for $*$–orderings
Annales de la faculté des sciences de Toulouse Sér. 6, 17 no. 1 (2008), p. 81-92, doi: 10.5802/afst.1177
Article PDF | Reviews MR 2464095 | Zbl pre05380230

We prove the $*$–version of the Joly–Becker theorem: a skew field admits a $*$–ordering of level $n$ iff it admits a $*$–ordering of level $n \ell $ for some (resp. all) odd $\ell \in \mathbb{N}$. For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a $*$–ordering of higher level also admits a $*$–ordering of level $1$. Every field that admits a $*$–ordering of higher level admits a $*$–ordering of level $1$ or $2$

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