Abstract
Let R be a finite commutative ring. The set F(R) of polynomial functions on R is a finite commutative ring with pointwise operations. Its group of units F(R) × is just the set of all unit-valued polynomial functions. We investigate polynomial permutations on R[x] / (x 2) = R[α] , the ring of dual numbers over R, and show that the group P R(R[α]) , consisting of those polynomial permutations of R[α] represented by polynomials in R[x], is embedded in a semidirect product of F(R) × by the group P(R) of polynomial permutations on R. In particular, when R= F q, we prove that PFq(Fq[α])≅P(Fq)⋉θF(Fq)×. Furthermore, we count unit-valued polynomial functions on the ring of integers modulo p n and obtain canonical representations for these functions.
Originalsprache | englisch |
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Seiten (von - bis) | 521 - 537 |
Seitenumfang | 17 |
Fachzeitschrift | Applicable Algebra in Engineering, Communication and Computing |
Jahrgang | 34 |
Ausgabenummer | 3 |
Frühes Online-Datum | 29 Mai 2021 |
DOIs | |
Publikationsstatus | Veröffentlicht - Mai 2023 |
ASJC Scopus subject areas
- Angewandte Mathematik
- Algebra und Zahlentheorie