| 关于单位1-稳定秩的注记 |
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| 引用本文： | 陈焕艮.关于单位1-稳定秩的注记[J].杭州师范学院学报(自然科学版),2009,8(3):161-167. |
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| 作者姓名： | 陈焕艮 |
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| 作者单位： | 杭州师范大学理学院,浙江杭州,310036 |
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| 基金项目： | Foundation item： Supported by the Foundation of Hangzhou Normal University （2009.1） . |
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| 摘 要： | 假定I是环R的理想,称I满足单位1-稳定秩,如果ax＋b=1,a,x∈I,b∈R可推出有u∈U（R）使得a＋bu∈U（R）.文章给出几个理想满足单位1-稳定秩的特征,证明了该条件对于矩阵扩张,三角矩阵扩张是保持的,进一步讨论其它相关理想的单位1-稳定秩性质.
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| 关 键 词： | 单位1-稳定秩 矩阵扩张 三角矩阵 |
A Note on Unit 1-Stable Rank |
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| CHEN Huan-yin.A Note on Unit 1-Stable Rank[J].Journal of Hangzhou Teachers College(Natural Science),2009,8(3):161-167. |
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| Authors: | CHEN Huan-yin |
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| Institution: | CHEN Huan-yin (College of Science, Hangzhou Normal University, Hangzhou 310036, China) |
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| Abstract: | Let I be an ideal of a ring R,I is said to satify unit 1-stable rank provided that ax+b=1 with a,x∈I,b∈R implies that a+bu∈U(R)for a u∈U(R).The paper investigates several equivalent characterizations of such conditions,Unit 1-stable rank iS studied for related ideals as well. |
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| Keywords: | unit 1-stable rank matrix extension triangular matrix |
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