  A main contribution of this paper is the explicit construction of comparison
morphisms between the standard bar resolution and Bardzell's minimal resolution
for truncated quiver algebras (TQA's).
  As a direct application we describe explicitely the Yoneda product and derive
several results on the structure of the cohomology ring of TQA's. For instance,
we show that the product of odd degree cohomology classes is always zero. We
prove that TQA's associated with quivers with no cycles or with neither sinks
nor sources have trivial cohomology rings. On the other side we exhibit a
fundamental example of a TQA with non trivial cohomology ring. Finaly, for
truncated polyniomial algebras in one variable, we construct explicit
cohomology classes in the bar resolution and give a full description of their
cohomology ring.
