关于Z/p^nZ上置换多项式的一个注记(英文)

A Note on Permutation Polynomials over Z/p^nZ

设Z是整数环,2≤n∈Z是一个整数,p是一个奇素数.Z[X]是整系数一多元项式环,J∪Z[X]是剩余类环Z/pnZ的化零理想.作者用解析的观点首先证明了剩余类环Z/pnZ上的任一置换多项式的逆映射也是Z/pnZ上的置换多项式,从而从解析的角度证明了Z/pnZ上的置换多项式对于映射的复合运算及对模J的约化作成一个群.

Let Z be the ring of integers,n∈Z with n ≥2 and p be an odd prime.Let Z be the ring of polynomials over Z and J be the ideal of Z which annihilates the residue class ring Z/pnZ.By analytic viewpoint, the author gives a proof of the result that the inverse of any permutation polynomial over Z/pnZ can be represented by a polynomial and so all permutation polynomials over Z/pnZ form a group according to the operation of composite of maps and reduction mod J.