Abstract
Let [Formula: see text] denote the Leavitt path algebra associated to the finite graph [Formula: see text] and field [Formula: see text]. For any closed path [Formula: see text] in [Formula: see text], we define and investigate the uniserial, artinian, non-Noetherian left [Formula: see text]-module [Formula: see text]. The unique simple factor of each proper submodule of [Formula: see text] is isomorphic to the Chen simple module [Formula: see text]. In our main result, we classify those closed paths [Formula: see text] for which [Formula: see text] is injective. In this situation, [Formula: see text] is the injective hull of [Formula: see text].
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