INDECOMPOSABLE NON UNISERIAL MODULES OF LENGTH THREE

We investigate a particular class of indecomposable modules of length three, defined over a K–algebra, with a simple socle and two non isomorphic simple factor modules. These modules may have any projective dimension different from zero. On the other hand their composition factors may have any countable dimension as vector spaces over the underlying field K. Moreover their endomorphism rings are K–vector spaces of dimension ≤ 2.