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The Realization Problem for finitely generated refinement monoids

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URI: http://hdl.handle.net/10498/21544

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1907.03648.pdf (631.1Kb)
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Author/s
Ara, Pere; Bosa, Joan; Pardo, Enrique
Date
2019-07-08
Department
Matemáticas
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)).
Subjects
von Neumann regular ring; refinement monoid; realization problem; universal localization
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  • Artículos Científicos [2988]
  • Articulos Científicos Matemáticas [77]
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
This work is under a Creative Commons License Attribution-NonCommercial-NoDerivatives 4.0 Internacional

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