On *-Semiordering

Abstract

We are given a division ring with involution D and a linear ordering > of the additive group S of all symmetric elements of D such that the unity of D is positive. We assume, further, that for every nonzero element x of D, and every positive elements of S, both xsx* and xx*s + sxx* are positive. We show among other things that > is in fact a *-semiordering provided its associated order valuation is compatible.

Notes

Communicated by A. Wadsworth.

*Dedicated to the memory of Joseph Chacron, my twin brother.