In this paper, we determine the structure of rings that have secondary representation (called representable rings) and give some characterizations of these rings. Also, we characterize Artinian rings in terms of representable rings. Then we introduce completely representable modules, modules every non-zero submodule of which have secondary representation, and give some necessary and sufficient conditions for a module to be completely representable. Finally, we define strongly representable modules and give some conditions under which representable module is strongly representable.

Keywords: Secondary modules, Secondary representation, Representable rings and modules, Laskerian rings and modules, Semiperfect rings, Artinian rings, Noetherian spectrum, Compactly packed rings, Q-rings, AB5^* modules, Linearly compact modules.