In this paper, we introduce notions of RLA-local modules and locally artinian supplemented modules which are proper generalizations as notions of strongly local modules and ss-supplemented modules, respectively and we study some properties of these module. In particular, we give a characterization of semi perfect rings and left perfect rings.

In this paper, we define semi-ss−discrete and quasi-ss−discrete modules as a strongly notion of semi-discrete and quasi-discrete modules with the help of ss−supplement in [3]. We examined the basic properties of these modules and included characterization of strongly ss−discrete modules over semi-perfect rings.