On duo rings, pure semisimplicity and finite representation type

In this note, we prove through a short and direct argument, that in left pure semisimple local rings, the two-sided ideals are principal. In particular, these rings are left (resp. right) uniserial if and only if they are left (resp. right) duo. As a corollary we obtain that if a ring is a counter-example to the pure semisimple conjecture, then it cannot be a duo ring.