Refinement monoids and adaptable separated graphs
Rings and Algebras
2019-04-10 v1 Operator Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.1904.04255,
title = {Refinement monoids and adaptable separated graphs},
author = {P. Ara and J. Bosa and E. Pardo},
journal= {arXiv preprint arXiv:1904.04255},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1606.03862