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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… Click to show full abstract
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).
Keywords:
numbers residue;
residue class;
rings dual;
dual numbers;
polynomial functions;
functions rings
Journal Title: Mathematica Slovaca
Year Published: 2021
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Journal Title: Mathematica Slovaca
Year Published: 2021
Link to full text (if available)
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recommendations!