On (alpha)-semi-Short Modules

We introduce and study the concept of alpha semi short modules. Using this concept we extend some of the basic results of alpha short modules to alpha semi short modules. We observe that if M is an alpha semi short module then the dual perfect dimension of M is alpha or alpha +1.  In particular, if a semiprime ring R is alpha semi short as an Rmodule, then its Noetherian dimension either is alpha or alpha +1.