I have tried to prove the statement that if an R-module is co-isosimple, then it is co-cyclic. In the paper that this stated, this is mentioned as since a co-isosimple module is artinian and uniserial, so is co-cyclic, but this is not clear for me. I need some hints for the proof.
If a non-zero module $M$ is isomorphic to all its non-zero quotients,then it is called $\textbf{co-isosimple}$.
A module $M$ is called $\textbf{co-cyclic}$ if there is a simple module that is essential in M.
To improve my question: I know that every Artinian module has a simple submodule and every submodule of a uniserial module is essential. Therefore if a module is both Artinian and uniserial, then it has a simple essential submodule, that is, it is co-cyclic. Furthermore, I've just realized that a co-isosimple module has uniserial dimension 1 so is a co-isosimple module is uniserial. However, I haven't proved that part, a co-isosimple module is Artinian, so I still need some hints for this one.