Conjugacy Classes and Invariant Subrings of R-Automorphisms of R[x]

We consider the group G of R-automorphisms of the polynomial ring Rx] in the case where the ring R has nonzero nilpotent elements. Little is known about G in this case, and because of the importance of G in understanding questions involving the polynomial ring Rx], we initiate here several lines of investigation. We do this by examining in detail examples involving the ring of integers modulo n. If R is a local ring with maximal ideal m such that R/m = ?₂ and m ² = (0), we describe more explicitly the structure of G and determine all rings of invariants of Rx] with respect to subgroups of G.