  Exceptional modules are tree modules. A tree module usually has many tree
bases and the corresponding coefficient quivers may look quite differently. The
aim of this note is to introduce a class of exceptional modules which have a
distinguished tree basis, we call them radiation modules (generalizing an
inductive construction considered already by Kinser). For a Dynkin quiver,
nearly all indecomposable representations turn out to be radiation modules, the
only exception is the maximal indecomposable module in case E_8. Also, the
exceptional representation of the generalized Kronecker quivers are given by
radiation modules. Consequently, with the help of Schofield induction one can
display all the exceptional modules of an arbitrary quiver in a nice way.
