BROWSE

Author Profile

Browsing by Subject F(R)

Jump to: 0-9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
or enter first few letters:  
Showing results [1 - 1] / 1
    • On the group of unit-valued polynomial functions
    Authors: Amr Ali, Al-Maktry;  Advisor: -;  Co-Author: - (2021)

    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 obtai...