Algebras with small homological dimensions

We consider the algebras Lambda which satisfy the property that for each in decomposable module X, either its projective dimension pd(Lambda)X is at mo st one or its injective dimension id(Lambda)X is at most one. This clearly generalizes the so-called quasitilted algebras introduced by Happel-Reiten- Smalo. We show that some of the niciest features for this latter class of a lgebras can be generalized to the case we are considering, in particular th e existence of a trisection in its module category.