  Considering forward dijet production in the $q\to qg$ partonic process, we
derive the spectrum of accompanying soft gluon radiation induced by
rescatterings in a nuclear target. The spectrum is obtained to logarithmic
accuracy for an arbitrary energy sharing between the final quark and gluon, and
for final transverse momenta as well as momentum imbalance being large as
compared to transverse momentum nuclear broadening. In the case of equal energy
sharing and for approximately back-to-back quark and gluon transverse momenta,
we reproduce a previous result of Liou and Mueller. Interpreting our result, we
conjecture a simple formula for the medium-induced radiation spectrum
associated to hard forward $1 \to n$ processes, which we explicitly check in
the case of the $g \to gg$ process.
