摘要
结合多项式剩余类环中元素整除性质,利用中国剩余定理构造了多项式剩余类环与局部环直和之间的同构映射,得到了相应的直和分解,在此基础上将一般剩余类环中幂零元计数问题进行了优化.通过引入广义Euler函数、多项式系数公因子等概念,提出了系数公因子为1的剩余类代表元计数方法,最后,给出了素数幂阶剩余类环中幂零元的计数表达式.
In this paper,the isomorphic mapping between polynomial residue class ring and direct sum of local ring is constructed by using Chinese Remainder Theorem,and the corresponding direct sum decomposition is obtained.On this basis,the enumeration problem of nilpotent elements in general residue class rings is optimized.The concepts of generalized Euler function and common factor of polynomial coefficients are introduced.It proposes the counting method of representative elements of residue class with common factor of 1.Finally,the counting expression of nilpotent elements in residue class rings of prime power order is given.
作者
田东代
TIAN Dong-dai(Heze Sports Training Center of Shandong Province, Heze Shandong 274000,China)
出处
《菏泽学院学报》
2021年第2期11-15,共5页
Journal of Heze University
关键词
幂零元
反演公式
直和分解
局部环
nilpotent element
inversion formula
direct sum decomposition
local ring
