Theorem

When a Leavitt path algebra is von Neumann regular

For any field $K$ and graph $E$, TFAE: 1) the Leavitt path algebra $L_K(E)$ is von Neumann regular; 2) $L_K(E)$ is strongly π-regular; 3) $E$ is an acyclic graph.

Reference(s)

  • G. Abrams, J. Bell, and K. Rangaswamy. On prime nonprimitive von Neumann regular algebras. (2014) @ Theorem 1 p 329