Abstract:In this paper we completely describe graphically Leavitt path algebras with bounded index of nilpotence. We show that the Leavitt path algebra LK (E) has index of nilpotence at most n if and only if no cycle in the graph E has an exit and there is a fixed positive integer n such that the number of distinct paths that end at any given vertex v (including v, but not including the entire cycle c in case v lies on c) is less than or equal to n. Interestingly, the Leavitt path algebras having bounded index of nilpo… Show more
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