Refinement monoids and adaptable separated graphs

We define a subclass of separated graphs, the class of adaptable separated graphs , and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and we explicitly determine their associated I -systems. We also show that any finitely generated conic...

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Bibliographic Details
Published in:Semigroup forum 2020-08, Vol.101 (1), p.19-36
Main Authors: Ara, Pere, Bosa, Joan, Pardo, Enrique
Format: Article
Language:English
Subjects:
Algebra
Graphical representations
Graphs
Mathematics
Mathematics and Statistics
Monoids
Research Article
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Summary:We define a subclass of separated graphs, the class of adaptable separated graphs , and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and we explicitly determine their associated I -systems. We also show that any finitely generated conical refinement monoid can be represented as the monoid of an adaptable separated graph. These results provide the first step toward an affirmative answer to the Realization Problem for von Neumann regular rings, in the finitely generated case.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-019-10077-2