关于循环环的自同构群的若干结论

Some Conclusions of Automorphism Groups of Cyclic Rings

借助循环环的性质和群的同态性质证明了循环环的满同态映射的一个性质,并借助这个性质证明了循环环的自同构群是交换群和循环环的自同构群的阶的计算公式.讨论了无限循环环的自同构群.设p、q为不同素数,分别讨论了自同构群为单位元群、素数阶群、pq阶群和p2阶群的有限循环环的类型.

A property of automorphism of cyclic rings was given from the properties of cyclic rings and group automorphism in the paper.It was proved that the automorphism groups of cyclic rings are abelian groups.The formula for the order of automorphism group of cyclic ring was also present.The automorphism group of infinite cyclic ring was gotten.Given two distrinct primes pand q,the type of cyclic rings of automorphism group with order one,prime,pqand p2 were also studied respectively.