Prüfer modules over Leavitt path algebras

Let LK(E) denote the Leavitt path algebra associated to the finite graph E and field K. For any closed path c in E, we define and investigate the uniserial, artinian, non-Noetherian left LK(E)-module U_{E,c−1}. The unique simple factor of each proper submodule of U_{E,c−1}is isomorphic to the Chen simple module V_[c∞]. In our main result, we classify those closed paths c for which U_{E,c−1} is injective. In this situation, U_{E,c−1} is the injective hull of V_[c∞].