研究在模n剩余类环的单位群结构给定的前提下如何确定Zn的问题.通过群论、环论及初等数论相关知识的运用,证明了U(Zn)可分解为阶为给定素数q1,q2,…,qm的循环群的直和时n的一个取值上界,并给出该结论的部分应用.
This paper considers how to determine the natural number n on the basis of the structure of U(Zn).By using the relative knowledge such as group theory,ring theory and number n theory,it gets a upper bound value of n when the U(Zn)can be decomposed into direct sum of cyclic groups with the order being qi(i=1,2,…,m),and also gets some applications of this conclusion.