  We show that a collection of generalized Bowen-Franks group, what we call the
principal Bowen-Franks $R$-modules, form a complete set of $R$-module
invariants for the equivalence relation of profinite conjugacy for similar
hyperbolic toral automorphisms. We also show that these principal generalized
Bowen-Franks $R$-modules are the principal invariants in a large class of
generalized Bowen-Franks $R$-module invariants for similar hyperbolic
automorphisms. We further show how the conjugacy invariant of cyclicity, when
applied to hyperbolic toral automorphisms, is realized for profinite conjugacy.

Dynamical Systems