The regular algebra of a quiver

Abstract

Let K be a fixed field. We attach to each column-finite quiver E a von Neumann regular K-algebra $Q(E)$ in a functorial way. The algebra $Q(E)$ is a universal localization of the usual path algebra $P(E)$ associated with E. The monoid of isomorphism classes of finitely generated projective right $Q(E)$-modules is explicitly computed.