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).
This work was supported by the Austrian Science Fund FWF projects P 27816-N26 and P 30934-N35.
Funding statement: The second and third authors wish to dedicate this paper to the memory of Prof. Al-Ezeh, who died while the paper was under review
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(Communicated by István Gaál)
Acknowledgement
The authors would like to thank Irena Swanson for valuable suggestions and comments on earlier versions of the manuscript.
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© 2021 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
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- Solvability of a nonlinear three-dimensional system of difference equations with constant coefficients
- Properties of critical and subcritical second order self-adjoint linear equations
- Korovkin type approximation via statistical e-convergence on two dimensional weighted spaces
- Approximation by a new sequence of operators involving Apostol-Genocchi polynomials
- Poisson like matrix operator and its application in p-summable space
- On the homological and algebraical properties of some Feichtinger algebras
- Disjoint topological transitivity for weighted translations generated by group actions
- On simultaneous limits for aggregation of stationary randomized INAR(1) processes with poisson innovations
- Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications
- The shifted Gompertz-G family of distributions: Properties and applications
- On the testing hypothesis in uniform family of distributions with nuisance parameter
- Clarkson inequalities related to convex and concave functions
Artikel in diesem Heft
- Regular papers
- Algebraic structures for pairwise comparison matrices: Consistency, social choices and Arrow’s theorem
- Polynomial functions on rings of dual numbers over residue class rings of the integers
- Sufficient conditions for p-valent functions
- Upper bounds for analytic summand functions and related inequalities
- Global structure for a fourth-order boundary value problem with sign-changing weight
- On the nonexistence conditions of solution of two-point in time problem for nonhomogeneous PDE
- Solvability of a nonlinear three-dimensional system of difference equations with constant coefficients
- Properties of critical and subcritical second order self-adjoint linear equations
- Korovkin type approximation via statistical e-convergence on two dimensional weighted spaces
- Approximation by a new sequence of operators involving Apostol-Genocchi polynomials
- Poisson like matrix operator and its application in p-summable space
- On the homological and algebraical properties of some Feichtinger algebras
- Disjoint topological transitivity for weighted translations generated by group actions
- On simultaneous limits for aggregation of stationary randomized INAR(1) processes with poisson innovations
- Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications
- The shifted Gompertz-G family of distributions: Properties and applications
- On the testing hypothesis in uniform family of distributions with nuisance parameter
- Clarkson inequalities related to convex and concave functions