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- W2554588713 abstract "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 $d$." @default.
- W2554588713 created "2016-11-30" @default.
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- W2554588713 date "2016-11-23" @default.
- W2554588713 modified "2023-09-27" @default.
- W2554588713 title "Leavitt path algebras with bounded index of nilpotence and simple modules over them" @default.
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