循环环的子结构、商结构以及特殊元素

The substructure,quotient structure and special elements of cyclic rings

首先讨论了文中所需的关于循环环和剩余类环的基本结果,然后借助这些结果对于循环环的子结构、商结构以及特殊元素进行了分析.关于子结构问题,给出了任意循环环的全部子环、理想、极大理想、素理想;关于商结构问题,讨论了商环的结构和商环为域的条件;也讨论了循环环中的单位元素、零因子元素、可逆元素、幂等元素、幂零元素等特殊元素的性质;给出了循环环的自同构群的阶的计算公式.

For any cyclic ring R, all of its subrings, ideals, maximal ideals, prime ideals of s were given in this paper. The construction of quotient rings of cyclic ring and the properties such that the quotient rings were fields were discussed. The properties of special elements in cyclic rings, such as unit element, zero factor elements, irreversible element, idempotent elements and nilpotent elements were stu^tied. The formula for the order of auto- morphism group of cyclic ring were also present in the paper.