The realization problem for finitely generated refinement monoids (Q2190733)

Based on authors' abstract: In this paper, the authors proved that every finitely generated conical refinement monoid can be represented as the monoid \(V(R)\) of isomorphism classes of finitely generated projective modules over a von Neumann regular ring \(R\). Further, they proved that there is a natural isomorphism between the separated graph monoid \(M(E, C)\) and the monoid \(V(Q_K (E, C))\) where \(Q_K (E, C)\) a von Neumann regular \(K\)-algebra.