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 language | English |
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Pages (from-to) | 1063-1088 |
Number of pages | 26 |
Journal | Mathematica Slovaca |
Volume | 71 |
Issue number | 5 |
DOIs | |
Publication status | Published - 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
- General Mathematics