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arXiv · 1907.03648

The Realization Problem for Finitely Generated Refinement Monoids

Pere Ara·Joan Bosa·Enrique Pardo
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Abstract

We show that every finitely generated conical refinement monoid can be represented as the monoid $\mathcal V(R)$ 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 $\mathcal V(Q_K (E, C))$.

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Pere Ara, Joan Bosa, Enrique Pardo. 2019-07-08. The Realization Problem for Finitely Generated Refinement Monoids. https://arxiv.org/abs/1907.03648

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