One knows that the bricks for a quiver are parametrised by the Schur rays, that is, the $1$-dimensional subspaces of the space of dimension vectors that contain a Schur root. One can show fairly easily that the endomorphism rings of the bricks are `stably free division rings' and it is an interesting question to know whether they are actually free division rings. This question takes on greater importance from the realisation that this problem is equivalent to describing the function fields of the moduli spaces of representations of the quiver of all dimension vectors lying in the Schur ray. Thus I show that these endomorphism rings are in fact free division rings and that if $\alpha$ is a Schur root then a moduli space of representations of dimension vector $\alpha$ is birational to $n$ $h$ by $h$ matrices up to simultaneous conjugacy where $h = \gcd_v(\alpha(v))$ and $n = 1 - \langle \beta, \beta \rangle$ where $\beta = \alpha/h$.
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Last modified: 17-08-1998