  The 3-Kronecker quiver has two vertices, namely a sink and a source, and 3
arrows. A regular representation of a representation-infinite quiver such as
the 3-Kronecker quiver is said to be elementary provided it is non-zero and not
a proper extension of two regular representations. Of course, any regular
representation has a filtration whose factors are elementary, thus the
elementary representations may be considered as the building blocks for
obtaining all the regular representations. We are going to determine the
elementary $3$-Kronecker modules. It turns out that all the elementary modules
are combinatorially defined.
