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

Xiumei Li; Min Sha

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arXiv · 1807.02379

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

Xiumei Li·Min Sha

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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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Xiumei Li, Min Sha. 2018-07-06. Congruence preserving functions in the residue class rings of polynomials over finite fields. https://arxiv.org/abs/1807.02379

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