On $\alpha $-semi-Short Modules

Document Type : Original Manuscript


Department of Mathematics, Shahid Chamran University of Ahvaz, P.O. Box: 6135713895, Ahvaz, Iran.


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 $\alpha +1$.