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arXiv · 1707.03732

Pr\"ufer modules over Leavitt path algebras

Gene Abrams·Francesca Mantese·Alberto Tonolo
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Abstract

Let $L_K(E)$ 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 $L_K(E)$-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 $V_{[c^\infty]}$. 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 $V_{[c^\infty]}$.

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Gene Abrams, Francesca Mantese, Alberto Tonolo. 2017-07-12. Pr\"ufer modules over Leavitt path algebras. https://arxiv.org/abs/1707.03732

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