Let LK(E) denote the Leavitt path algebra associated to the finite graph E and field K. For any cycle c in E, we define and investigate the uniserial, artinian, non- noetherian left LK(E)-module UE,c−1. The unique simple factor of each proper submodule of UE,c−1 is isomorphic to the Chen simple module V[c∞]. In our main result, we classify those cycles c for which UE,c−1 is injective. In this situation, UE,c−1 is the injective hull of V[c∞].
Prüfer modules over Leavitt path algebras
Mantese, Francesca;
2019-01-01
Abstract
Let LK(E) denote the Leavitt path algebra associated to the finite graph E and field K. For any cycle c in E, we define and investigate the uniserial, artinian, non- noetherian left LK(E)-module UE,c−1. The unique simple factor of each proper submodule of UE,c−1 is isomorphic to the Chen simple module V[c∞]. In our main result, we classify those cycles c for which UE,c−1 is injective. In this situation, UE,c−1 is the injective hull of V[c∞].
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