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arXiv · 1606.03862

Representing finitely generated refinement monoids as graph monoids

P. Ara·E. Pardo
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Abstract

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.

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P. Ara, E. Pardo. 2016-06-13. Representing finitely generated refinement monoids as graph monoids. https://doi.org/10.1016/j.jalgebra.2017.02.007

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