摘要
设R是有单位元的结合环,Ks(R)为以s为乘子的广义矩阵环,其中s为R的中心元素.记Rqnil为环R的所有拟幂零元构成的集合.借助交换环上广义矩阵环的凯莱—哈密尔顿定理证明了环R为交换环时Ks(R)qnil与R的Jacobson根之间的关系,改进了王周和陈建龙2012年给出的交换环上矩阵环的相应结果.
Let R be an associative ring with identity, and let Ks （R） be the generalized matrix ring over R where s is in the center of R. The set of all of the quasi-nilpotent elements of R was denoted by Rq＂i~. The quasi-nilpotent elements of generalized matrix rings Ks （R） over a commutative local ring R was mainly studied using the Cayley-Hamilton theorem over genenralized matrix rings. The relation between Ks （R） qnil and the Jacobson radical of R was given. The corresponding result of matrix rings over commut- ative rings was improved.
出处
《郑州大学学报（理学版）》
CAS
北大核心
2013年第3期6-8,12,共4页
Journal of Zhengzhou University:Natural Science Edition
基金
国家数学天元青年基金资助项目
编号11226071
关键词
广义矩阵环
拟幂零元
JACOBSON根
局部环
generalized matrix ring
quasi-nilpotent elements
Jacobson radical
local ring
