Resumen de The realization problem for finitely generated refinement monoids

Pere Ara , Joan Bosa, Enrique Pardo Espino

• We show 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. To this end, we use the representation of these monoids provided by adaptable separated graphs. Given an adaptable separated graph (E, C) and a field K, we build a von Neumann regular K-algebra QK(E,C) and show that there is a natural isomorphism between the separated graph monoid M(E, C) and the monoid V(QK(E,C)).