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
ABSTRACTS VIEWS

16

FULLTEXT VIEWS

8

Files in This Item:

Thumbnail
  • On the group of unit-valued polynomial functions-2021.pdf
      Restricted Access
    • Size : 1,73 MB

    • Format : Adobe PDF