I need an example of a module that is finitely generated, finitely cogenerated and also linearly compact (in discrete topology) but not Artinian.
In fact I proved a theorem with this strong assumptions and I am not sure that there is such a module except finitely generated Artinian modules (and my result for finitely generated Artinian modules is obvious). For the definition of finitely cogenerated modules one can see https://en.wikipedia.org/wiki/Finitely_generated_module. Can anyone give me such an example. Thanks a lot.