Congruence preserving functions in the residue class rings of polynomials over finite fields

Abstract

In this paper, as an analogue of the integer case, we define congruence preserving functions over the residue class rings of polynomials over finite fields. We establish a counting formula for such congruence preserving functions, determine a necessary and sufficient condition under which all congruence preserving functions are also polynomial functions, and characterize such functions.

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