The realization problem for finitely generated refinement monoids

  1. Pere Ara 1
  2. Joan Bosa 1
  3. Enrique Pardo Espino 2
  1. 1 Universitat Autònoma de Barcelona, España
  2. 2 Universidad de Cádiz, España
Journal:
Selecta Mathematica, New Series

ISSN: 1022-1824

Year of publication: 2020

Volume: 26

Issue: 3

Pages: 17

Type: Article

DOI: 10.1007/S00029-020-00559-5 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Selecta Mathematica, New Series

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 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)).

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