Resumen de The Leavitt path algebras of arbitrary graphs

Gene Abrams , Gonzalo Aranda Pino

• We extend the notion of the Leavitt path algebra of a graph to include all directed graphs. We show how various ring-theoretic properties of these more general structures relate to the corresponding properties of Leavitt path algebras of row-finite graphs. Specifically, we identify those graphs for which the corresponding Leavitt path algebra is simple; purely infinite simple; exchange; and semiprime. In our final result, we show that all Leavitt path algebras have zero Jacobson radical.