  In 1996, Franke constructed a purely algebraic category that is equivalent as
a triangulated category to the E(n)-local stable homotopy category for n^2+n <
2p-2. The two categories are not Quillen equivalent, and his proof uses systems
of triangulated diagram categories rather than model categories. Our main
result is that in the case n=1 Franke's functor maps the derived tensor product
to the smash product. It can however not be an associative equivalence of
monoidal categories. The first part of our paper sets up a monoidal version of
Franke's systems of triangulated diagram categories and explores its
properties. The second part applies these results to the specific construction
of Franke's functor in order to prove the above result.
