The realization problem for finitely generated refinement monoids
- Pere Ara 1
- Joan Bosa 1
- Enrique Pardo Espino 2
- 1 Universitat Autònoma de Barcelona, España
- 2 Universidad de Cádiz, España
ISSN: 1022-1824
Año de publicación: 2020
Volumen: 26
Número: 3
Páginas: 17
Tipo: Artículo
Otras publicaciones en: Selecta Mathematica, New Series
Resumen
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)).