RT journal article
T1 The Realization Problem for finitely generated refinement monoids
A1 Ara, Pere
A1 Bosa, Joan
A1 Pardo Espino, Enrique
A2 Matemáticas
K1 von Neumann regular ring
K1 refinement monoid
K1 realization problem
K1 universal localization
AB 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)).
PB arXiv.org
YR 2019
FD 2019-07-08
LK http://hdl.handle.net/10498/21544
UL http://hdl.handle.net/10498/21544
LA eng
NO 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.
DS Repositorio Institucional de la Universidad de Cádiz
RD 13-nov-2026