Strong perforation in infinitely generated K_0-groups of simple C^*-algebras - Toms, Andrew S. (MATHEMATICA SCANDINAVICA, 2005)
Let (G,G^+) be an ordered abelian group. We say that G has strong perforation if there exists x G, x otin G^+, such that nx G^+, nx eq 0 for some natural number n. Otherwise, the group is said to be weakly unperforated. Examples of simple C^*-algebras whose ordered K_0-groups have this property and for which the entire order structure on K_0 is known have, until now, been restricted to the case where K_0 is group isomorphic to the integers. We construct simple, separable, unital C^*-algebras with strongly perforated K_0-groups group isomorphic to an arbitrary infinitely generated subgroup of the rationals, and determine the order structure on K_0 in each case.