Let *D* be a skew field that is central and finite-dimensional over a number field *F* (in particular: a quaternion algebra over F). Let $\Delta$ $\subseteq$ *D* be a maximal $\mathcal{O}$$_{F}$-order. Let $\mathfrak{b}$ be a fractional left $\Delta$-ideal and say we have a $\mathbb{Z}$-basis $\omega_1, . . . , \omega_n$ for $\Delta$ with $\omega_1 = 1$.

According to the definition of fractional ideals, we can find *d* $\in$ $\Delta$ such that *d*$\mathfrak{b}$ (or $\mathfrak{b}$*d*?) $\subseteq$ $\Delta$.

Given this setting, what do we know about *d*? A paper I have recently read has led me to believe that *d* $\in$ $\mathbb{Z}$ but I don't see why that would be the case.