Polynomial functions on rings of dual numbers over residue class rings of the integers

Hasan Al-Ezeh, Amr Ali Abdulkader Al-Maktry*, Sophie Frisch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The ring of dual numbers over a ring R is R[α] = R[x]/(x2), where α denotes x + (x2). For any finite commutative ring R, we characterize null polynomials and permutation polynomials on R[α] in terms of the functions induced by their coordinate polynomials (f1, f2 ∈ R[x], where f = f1 + αf2) and their formal derivatives on R. We derive explicit formulas for the number of polynomial functions and the number of polynomial permutations on Zpn[α] for n ≤ p (p prime).

Original languageEnglish
Pages (from-to)1063-1088
Number of pages26
JournalMathematica Slovaca
Volume71
Issue number5
DOIs
Publication statusPublished - 1 Oct 2021

Keywords

  • dual numbers
  • finite commutative rings
  • finite rings
  • null polynomials
  • permutation polynomials
  • polynomial functions
  • polynomial mappings
  • polynomial permutations
  • polynomials

ASJC Scopus subject areas

  • Mathematics(all)

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