On the group of unit-valued polynomial functions
CC BY
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2023
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oai:localhost:PNK-83122023-04-26T02:40:24Z On the group of unit-valued polynomial functions Amr Ali, Al-Maktry F(R) R[x]/(x2)=R[α] CC BY 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]/(x2)=R[α], the ring of dual numbers over R, and show that the group PR(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=Fq , we prove that PFq(Fq[α])≅P(Fq)⋉θF(Fq)×. Furthermore, we count unit-valued polynomial functions on the ring of integers modulo pn and obtain canonical representations for these functions. 2023-04-26T02:40:24Z 2023-04-26T02:40:24Z 2021 Book https://link.springer.com/article/10.1007/s00200-021-00510-x https://dlib.phenikaa-uni.edu.vn/handle/PNK/8312 en application/pdf Springer |
| institution |
Digital Phenikaa |
| collection |
Digital Phenikaa |
| language |
English |
| topic |
F(R) R[x]/(x2)=R[α] |
| spellingShingle |
F(R) R[x]/(x2)=R[α] Amr Ali, Al-Maktry On the group of unit-valued polynomial functions |
| description |
CC BY |
| format |
Book |
| author |
Amr Ali, Al-Maktry |
| author_facet |
Amr Ali, Al-Maktry |
| author_sort |
Amr Ali, Al-Maktry |
| title |
On the group of unit-valued polynomial functions |
| title_short |
On the group of unit-valued polynomial functions |
| title_full |
On the group of unit-valued polynomial functions |
| title_fullStr |
On the group of unit-valued polynomial functions |
| title_full_unstemmed |
On the group of unit-valued polynomial functions |
| title_sort |
on the group of unit-valued polynomial functions |
| publisher |
Springer |
| publishDate |
2023 |
| url |
https://link.springer.com/article/10.1007/s00200-021-00510-x https://dlib.phenikaa-uni.edu.vn/handle/PNK/8312 |
| _version_ |
1764268033488977920 |
| score |
8.887836 |