  We study invariants for shifts of finite type obtained as the K-theory of
various C*-algebras associated with them. These invariants have been studied
intensely over the past thirty years since their introduction by Wolfgang
Krieger. They may be given quite concrete descriptions as inductive limits of
simplicially ordered free abelian groups. Shifts of finite type are special
cases of Smale spaces and, in earlier work, the second author has shown that
the hyperbolic structure of the dynamics in a Smale space induces natural ring
and module structures on certain of these K-groups. Here, we restrict our
attention to the special case of shifts of finite type and obtain explicit
descriptions in terms of the inductive limits.
