Finitely generated antisymmetric graph monoids

JOURNAL OF ALGEBRA

卷:320

Article

Ara, Pere¹  Perera, Francesc¹  Wehrung, Friedrich² 

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

[2] Univ Caen, LMNO, CNRS, UMR 6139,Dept Math, F-14032 Caen, France

关键词: monoid;    commutative;    quiver;    graph monoid;    separative;    refinement;    primely generated;    primitive;    antisymmetric;    prime element;    free element;    regular element;    von Neumann regular;    C*-algebra;   

DOI  :  10.1016/j.jalgebra.2008.06.013

来源: Elsevier

【 摘 要 】

A graph monoid is a commutative monoid for which there is a particularly simple presentation, given in terms of a quiver. Such monoids are known to satisfy various nonstable K-theoretical representability properties for either von Neumann regular rings or C*-algebras. We give a characterization of graph monoids within finitely generated antisymmetric refinement monoids. This characterization is formulated in terms of the prime elements of the monoid, and it says that each free prime has at most one free lower cover. We also characterize antisymmetric graph monoids of finite quivers. In particular, the monoid Z(infinity) = {0, 1, 2,...} U {infinity} is a graph monoid, but it is not the graph monoid of any finite quiver. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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