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Representing finitely generated refinement monoids as graph monoids (1606.03862v3)
Published 13 Jun 2016 in math.RA, math.KT, and math.OA
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.