scholarly journals ON SEPARATIVE REFINEMENT MONOIDS

2009 ◽  
Vol 46 (3) ◽  
pp. 489-498 ◽  
Author(s):  
Huanyin Chen
Keyword(s):  
Author(s):  
Pere Ara ◽  
Joan Bosa ◽  
Enrique Pardo ◽  
Aidan Sims

Abstract Given an adaptable separated graph, we construct an associated groupoid and explore its type semigroup. Specifically, we first attach to each adaptable separated graph a corresponding semigroup, which we prove is an $E^*$-unitary inverse semigroup. As a consequence, the tight groupoid of this semigroup is a Hausdorff étale groupoid. We show that this groupoid is always amenable and that the type semigroups of groupoids obtained from adaptable separated graphs in this way include all finitely generated conical refinement monoids. The first three named authors will utilize this construction in forthcoming work to solve the realization problem for von Neumann regular rings, in the finitely generated case.


1984 ◽  
Vol 91 (1) ◽  
pp. 166-175 ◽  
Author(s):  
Hans Dobbertin
Keyword(s):  

2011 ◽  
Vol 363 (9) ◽  
pp. 4505-4525 ◽  
Author(s):  
Eduard Ortega ◽  
Francesc Perera ◽  
Mikael Rørdam

2019 ◽  
Vol 101 (1) ◽  
pp. 19-36 ◽  
Author(s):  
Pere Ara ◽  
Joan Bosa ◽  
Enrique Pardo
Keyword(s):  

2014 ◽  
Vol 91 (1) ◽  
pp. 1-27 ◽  
Author(s):  
P. Ara ◽  
K. R. Goodearl
Keyword(s):  

2020 ◽  
Vol 26 (3) ◽  
Author(s):  
Pere Ara ◽  
Joan Bosa ◽  
Enrique Pardo

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