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arXiv · 1603.09695

Leavitt path algebras having Unbounded Generating Number

G. Abrams·T. G. Nam·N. T. Phuc
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Abstract

We present a result of P. Ara which establishes that the Unbounded Generating Number property is a Morita invariant for unital rings. Using this, we give necessary and sufficient conditions on a graph $E$ so that the Leavitt path algebra associated to $E$ has UGN. We conclude by identifying the graphs for which the Leavitt path algebra is (equivalently) directly finite; stably finite; Hermite; and has cancellation of projectives.

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G. Abrams, T. G. Nam, N. T. Phuc. 2016-03-31. Leavitt path algebras having Unbounded Generating Number. https://arxiv.org/abs/1603.09695

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