摘要
由基本的群论知识可知剩余类环Z/pnZ上的置换多项式向量按映射的合成运算构成一个群,从而任一置换多项式向量的逆映射也是一个置换多项式向量.本注记则用分析的方法首先给出了Z/pnZ上任一置换多项式向量的逆映射也是一个置换多项式向量,从而得到Z/pnZ上的置换多项式向量按映射的合成运算构成一个群.这个结果推广了已有的结果.
By elementary theory of groups one can verify that the set of permutation polynomial vectors over the residue class ring Z/p^nZ is a group according to composite of mappings, hence the inverse of each permutation polynomial vector over Z/p^nZ is also a permutation polynomial vector. In this paper, by analytic viewpoint, the authors prove that the inverse of each permutation polynomial vector over Z/p^nZ is also a permutation polynomial vector, hence the set of permutation polynomial vectors over the residue class ring Z/p^nZ is a group according to composite of mappings.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2005年第5期896-900,共5页
Journal of Sichuan University(Natural Science Edition)
基金
四川省教育厅基金资助项目(2004B014)
关键词
置换多项式向量
剩余类环
群
permutation polynomial vector
residue class ring of integers
group
