The realization problem for finitely generated refinement monoids

• Pere Ara ^[1] ; Joan Bosa ^[1] ; Enrique Pardo ^[2]
  1. [1] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     
  2. [2] Universidad de Cádiz

     Universidad de Cádiz

     Cádiz, España

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 3, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-00559-5
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• 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)).