关于循环环的自同构群的若干结论  

Some Conclusions of Automorphism Groups of Cyclic Rings

作　　者：王骁力[1] 鲁丽萍[2] 谭冰[1] 

机构地区：[1]南阳师范学院数学与统计学院,河南南阳473061 [2]河南财政税务高等专科学校信息工程系,郑州450002

出　　处：《河南大学学报（自然科学版）》2014年第2期131-136,共6页Journal of Henan University:Natural Science

基　　金：国家自然科学基资助金项目(41306207;51349006);南阳师范学院专项资助项目(ZX2013015)

摘　　要：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.

关 键 词：循环环 自同构群 生成元素 阶 

分 类 号：O153.3[理学—数学]