Positivity in the narrow ray condition over the rationals

For an algebraic integer $a$ of $\mathbb Q$, positivity under every real embedding of $\mathbb Q$ is equivalent to positivity of the corresponding integer in $\mathbb Z$. This converts the archimedean condition in the narrow ray subgroup of $\mathbb Q$ into the usual positive-generator condition used to identify its ray classes with $(\mathbb Z/n\mathbb Z)^\times$.