| 广义矩阵环的拟幂零元 |
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| 引用本文： | 黄青鹤,应志领.广义矩阵环的拟幂零元[J].郑州大学学报(自然科学版),2013(3):6-8,12. |
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| 作者姓名： | 黄青鹤 应志领 |
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| 作者单位： | [1]江苏科技大学数理学院,江苏镇江212003 [2]南京邮电大学理学院,江苏南京210023 |
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| 基金项目： | 国家数学天元青年基金资助项目,编号11226071 |
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| 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.
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| 关 键 词： | 广义矩阵环 拟幂零元 Jacobson根 局部环 |
Quasi-nilpotent Elements of Generalized Matrix Rings |
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| HUANG Qing-het,YING Zhi-Ling.Quasi-nilpotent Elements of Generalized Matrix Rings[J].Journal of Zhengzhou University (Natural Science),2013(3):6-8,12. |
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| Authors: | HUANG Qing-het YING Zhi-Ling |
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| Institution: | 2 ( 1. School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, China ; 2. School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China) |
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| Abstract: | 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. |
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| Keywords: | generalized matrix ring quasi-nilpotent elements Jacobson radical local ring |
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