Leavitt path algebras are Bézout

Gene Abrams, Francesca Mantese, Alberto Tonolo

Let $E$ be a directed graph, $K$ any field, and let $L_K(E)$ denote the Leavitt path algebra of $E$ with coefficients in $K$. We show that $L_K(E)$ is a Bézout ring, i.e., that eve…