| 唯一强clean三角矩阵环 |
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| 引用本文： | 崔建,陈建龙. 唯一强clean三角矩阵环[J]. 东南大学学报, 2011, 0(4): 463-465 |
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| 作者姓名： | 崔建 陈建龙 |
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| 作者单位： | 东南大学数学系 |
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| 基金项目： | The National Natural Science Foundation of China(No.10971024);the Specialized Research Fund for the Doctoral Program of Higher Education(No.200802860024);the Natural Science Foundation of Jiangsu Province(No.BK2010393) |
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| 摘 要： | 称一个环R中的元素a是唯一强clean的,如果a可以唯一地表示成幂等元和可逆元的和且二者可交换.称环R是唯一强clean的,如果R中每一个元素都是唯一强clean元.研究了n×n阶三角矩阵环的唯一强clean性.设R为局部环,证明了环R上的任意n×n阶上三角矩阵环是唯一强clean的当且仅当R是唯一bleached的且...
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| 关 键 词： | 唯一强clean环 唯一bleached局部环 三角矩阵环 |
Uniquely strongly clean triangular matrix rings |
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| Cui Jian Chen Jianlong. Uniquely strongly clean triangular matrix rings[J]. Journal of Southeast University(English Edition), 2011, 0(4): 463-465 |
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| Authors: | Cui Jian Chen Jianlong |
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| Affiliation: | Cui Jian Chen Jianlong(Department of Mathematics,Southeast University,Nanjing 211189,China) |
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| Abstract: | An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute,and in addition,this expression is unique.R is called uniquely strongly clean if every element of R is uniquely strongly clean.The uniquely strong cleanness of the triangular matrix ring is studied.Let R be a local ring.It is shown that any n×n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J(R)≌Z2. |
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| Keywords: | uniquely strongly clean ring uniquely bleached local ring triangular matrix ring |
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