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 $R$-module, then its Noetherian dimension either is $alpha$ or $alpha +1$.