Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Leavitt path algebras with bounded index of nilpotence and simple
  modules over them   In this paper we completely describe graphically Leavitt path algebras with
bounded index of nilpotence and show that each graded simple module $S$ over a
Leavitt path algebra with bounded index of nilpotence is graded
$\Sigma$-injective, that is, $S^{(\alpha)}$ is graded injective for any
cardinal $\alpha$. Furthermore, we characterize Leavitt path algebras over
which each simple module is $\Sigma$-injective. We have shown that each simple
module over a Leavitt path algebra $L_K(E)$ is $\Sigma$-injective if and only
if the graph $E$ contains no cycles, and there is a positive integer $d$ such
that the length of any path in $E$ is less than or equal to $d$ and the number
of distinct paths ending at any vertex $v$ (including $v$) is less than or
equal to $d$.

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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg