%0 Journal Article 
%A Ara, Pere
%A Bosa, Joan
%A Pardo Espino, Enrique
%T The Realization Problem for finitely generated refinement monoids
%D 2019
%U http://hdl.handle.net/10498/21544
%X 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 Q_K(E,C) and show that there is a natural isomorphism between the separated graph monoid M(E,C) and the monoid V(Q_K(E,C)).
%K von Neumann regular ring
%K refinement monoid
%K realization problem
%K universal localization
%~ Universidad de Cádiz