sentences:  For any locally matricial algebra "R", "V(R)" is the positive cone of a so-called "dimension group".By definition, a dimension group is a partially ordered abelian group whose underlying order is directed, whose positive cone is a refinement monoid, and which is "unperforated", the letter meaning that "mx≥0" implies that "x≥0", for any element "x" of "G" and any positive integer "m".Any "simplicial" group, that is, a partially ordered abelian group of the form formula_8, is a dimension group.