An Iso M-Artinian (Noetherian) modules are the generalization of an iso Artinian (Noetherian) modules, which is described as every descending (ascending) chain of M-cyclic submodules terminates with respect to isomorphism i.e., \(g_{n}(M)\cong g_{n+1}(M)\) for all \(n\ge k\) after a finite index \(k\in \mathbb {N}\) , where \(g_{k}\in End (M)\) . We proved that if M be an isosimple injective R-module and N be an iso M-Artinian (Noetherian), then \(N\oplus M\) is an iso \((N\oplus M\) )-Artinian (Noetherian) R-module. For a ring R, we define an iso R-Artinian (Noetherian) ring, if it is an iso M-Artinian (Noetherian) module where M= \(_RR\) . Also we proved that for a commutative iso R-Artinian ring R, if every non-zero ideal of R possesses an idempotent element, then R is Noetherian.