  We compute the groupoid homology for the ample groupoids associated with
algebraic actions from rings of algebraic integers and integral dynamics. We
derive results for the homology of the topological full groups associated with
rings of algebraic integers, and we use our groupoid homology calculation to
compute the K-theory for ring C*-algebras of rings of algebraic integers,
recovering the results of Cuntz and Li and of Li and L\"uck without using
Cuntz--Li duality. Moreover, we compute the K-theory for C*-algebras attached
to integral dynamics, resolving the conjecture by Barlak, Omland, and Stammeier
in full generality.
