Let $R$ be an integral domain such that there is a total ordering of it. If $F$ is its field of fractions, is there a total ordering on $F$? In particular, is it naturally induced by that of $R$?
2026-03-26 06:21:25.1774506085
If an integral domain is ordered, is its field of fractions ordered?
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Say $\frac ab$ is positive if $ab$ is positive. Show that this is well-defined. Show that the sum and product of two positive fractions is positive. Show that the fractions are partitioned into positives, 0, and the additive inverses of positives.