Representing finitely generated refinement monoids as graph monoids

Graph monoids arise naturally in the study of non-stable K-theory of graph C*-algebras and Leavitt path algebras. They play also an important role in the current approaches to the realization problem for von Neumann regular rings. In this paper, we characterize when a finitely generated conical refi...

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Bibliographic Details
Published in:Journal of algebra 2017-06, Vol.480, p.79-123
Main Authors: Ara, Pere, Pardo, Enrique
Format: Article
Language:English
Subjects:
Graph monoid
Primely generated monoid
Refinement monoid
Regular monoid
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Summary:Graph monoids arise naturally in the study of non-stable K-theory of graph C*-algebras and Leavitt path algebras. They play also an important role in the current approaches to the realization problem for von Neumann regular rings. In this paper, we characterize when a finitely generated conical refinement monoid can be represented as a graph monoid. The characterization is expressed in terms of the behavior of the structural maps of the associated I-system at the free primes of the monoid.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2017.02.007