Functions and polynomials over finite commutative rings (Q5945044)

Let \(R\) be a finite commutative ring. The authors derive an upper bound for the total number of functions from \(R\) to itself which can be represented by polynomials over \(R\). This extends earlier results for Galois rings of \textit{J. V. Brawley} and \textit{G. L. Mullen} [J. Number Theory 41, No. 2, 156--166 (1992; Zbl 0759.11043)]. They also provide a necessary condition for equality.