Polynomial transformations of a GEO-ring of prime characteristic

Let $S$ be an arbitrary finite chain ring of prime characteristic. The aim of this paper is to describe the set of polynomial transformations and polynomial substitutions of $S$. The numbers of polynomial transformations and polynomial substitutions are found in some particular cases. We prove that if $S$ is non-commutative, then any polynomial transformation of $S$ is non-transitive.
The research was supported by grant 2358.2003.9 of the President of the Russian Federation for supporting the leading scientific schools.