模n的剩余类加群(Z_n,+)及模n剩余类环(Z_n,+,·)的若干性质

Some Characteristics of Remainder Plus Group(Zn, +) and Remainder Ring(Zn, +,.) of Mould N

模n剩余类加群是有限循环群的代表,在群论中占有重要地位,本文具体地给出模n的剩余类加群的生成元及其个数、子群个数、自同构个数;还给出了模n剩余类环的可逆元及其个数、子环个数、零因子个数等问题的解决。

The remainder plus group of Mould N represents the limited circulation group and plays a significant role in the theory of groups. This article points out specifically the number of resultant elements, sub - groups and self - identical structure of the remainder plus group of Mould N. It also puts forward the number of the reversible elements, sub - rings and zero factors as well as solutions to these problems.