On large indecomposable modules, endo-wild representation type and right pure semisimple rings

The existence of large indecomposable right $R$-modules over a right artinian ring $R$ is discussed in connection with the pure semisimplicity problem and the endo-wildness of the category ${\rm Mod}(R)$ of right $R$-modules. Some conjectures and open problems are presented.