@misc{10498/21544,
year = {2019},
month = {7},
url = {http://hdl.handle.net/10498/21544},
abstract = {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)).},
organization = {The three authors were partially supported by the DGI-MINECO and European Regional Development Fund, jointly, through the grant MTM2017-83487-P. The first and second authors were partially supported by the Generalitat de Catalunya through the grant 2017-SGR-1725. The first author was partially supported by the Beatriu de Pino ́s postdoctoral programme of the Government of Catalonia’s Secretariat for Universities and Research of the Ministry of Economy and Knowledge. The third author was partially supported by PAI III grant FQM-298 of the Junta de Andalucía.},
publisher = {arXiv.org},
keywords = {von Neumann regular ring},
keywords = {refinement monoid},
keywords = {realization problem},
keywords = {universal localization},
title = {The Realization Problem for finitely generated refinement monoids},
author = {Ara, Pere and Bosa, Joan and Pardo Espino, Enrique},
}