Dynamical systems arising from units in Krull rings

To a countable Krull ring R and units ξ1,…,ξd∈Rξ1,…,ξd∈R we associate a BbbZdBbbZd -action by automorphisms of the compact abelian group RˆR^ . This generalizes the 'S-integer' dynamical systems described by Chothi, Everest and Ward. We examine the extent to which some of their results extend and investigate the relationship between algebraic properties of R and dynamical properties of the associated action.