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

Xiumei Li, Min Sha*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Article number101604
Pages (from-to)1-15
Number of pages15
JournalFinite Fields and their Applications
Volume61
DOIs
Publication statusPublished - Jan 2020

Bibliographical note

Funding Information:
The authors are grateful to Professor Sophie Frisch for valuable discussions. For the research, the first author was supported by the National Science Foundation of China Grant No. 11526119 and the Scientific Research Foundation of Qufu Normal University No. BSQD20130139, and the second author was supported by a Macquarie University Research Fellowship.

Funding Information:
The authors are grateful to Professor Sophie Frisch for valuable discussions. For the research, the first author was supported by the National Science Foundation of China Grant No. 11526119 and the Scientific Research Foundation of Qufu Normal University No. BSQD20130139 , and the second author was supported by a Macquarie University Research Fellowship.

Publisher Copyright:
© 2019 Elsevier Inc.

Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

Keywords

  • Congruence preserving function
  • Polynomial function
  • Polynomials over finite fields
  • Residue class ring

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