  We study Van den Bergh's noncommutative symmetric algebra
$\mathbb{S}^{nc}(M)$ (over division rings) via Minamoto's theory of Fano
algebras. In particular, we show $\mathbb{S}^{nc}(M)$ is coherent, and its proj
category $\mathbb{P}^{nc}(M)$ is derived equivalent to the corresponding
bimodule species. This generalizes the main theorem of \cite{minamoto}, which
in turn is a generalization of Beilinson's derived equivalence. As corollaries,
we show that $\mathbb{P}^{nc}(M)$ is hereditary and there is a structure
theorem for sheaves on $\mathbb{P}^{nc}(M)$ analogous to that for
$\mathbb{P}^1$.
