%0 Journal Article 
%A Pardo Espino, Enrique
%A Wehrung, F.
%T Semilattices of groups and nonstable K-theory of extended Cuntz limits
%D 2006
%U http://hdl.handle.net/10498/16086
%X We give an elementary characterization of those abelian monoidsM
that are direct limits of countable sequences of finite direct sums of monoids
of the form either (Z/nZ) ⊔ {0} or Z ⊔ {0}. This characterization involves the
Riesz refinement property together with lattice-theoretical properties of the
collection of all subgroups of M (viewed as a semigroup), and it makes it pos-
sible to express M as a certain submonoid of a direct product  ×G, where  
is a distributive semilattice with zero and G is an abelian group. When applied
to the monoids V (A) appearing in the nonstable K-theory of C*-algebras, our
results yield a full description of V (A) for C*-inductive limits A of finite sums
of full matrix algebras over either Cuntz algebras On, where 2 ≤ n < ∞, or
corners of O1 by projections, thus extending to the case including O1 earlier
work by the authors together with K.R. Goodearl.
%~ Universidad de Cádiz