Leavitt path algebras having Unbounded Generating Number

2016/03/31 by Abrams, G., Nam, T. G., Phuc, N. T. · 1 citation
#05C25 #16S99 #18G05 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1603.09695

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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