In this article, we investigate the properties of chain conditions for modules and rings up to isomorphism, in the context of M-cyclic submodules and R-cyclic ideals respectively. Here, we introduce iso e-M-Noetherian modules, iso e-R-Noetherian rings and their dual structures and further discuss several characterizations of these rings and modules. We proved that R is an iso e-R-Noetherian ring if the direct sum of any collection of injective R-modules is itself injective.