Item Infomation
Title: |
On the group of unit-valued polynomial functions |
Authors: |
Amr Ali, Al-Maktry |
Issue Date: |
2021 |
Publisher: |
Springer |
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]/(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. |
Description: |
CC BY |
URI: |
https://link.springer.com/article/10.1007/s00200-021-00510-x https://dlib.phenikaa-uni.edu.vn/handle/PNK/8312 |
Appears in Collections |
OER - Công nghệ thông tin |
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