| 矩阵环的半交换子环 |
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| 引用本文： | 刘仲奎.矩阵环的半交换子环[J].数学研究及应用,2006,26(2):264-268. |
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| 作者姓名： | 刘仲奎 |
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| 作者单位： | 西北师范大学数学系,甘肃,兰州,730070 |
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| 基金项目： | the National Natural Science Foundation of China (10171082), TRAPOYT, and NWNUKJCXGC212 |
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| 摘 要： | 称环R是半交换的,如果对任意a∈R,rR(a)是R的理想．若n≥2,则任意具有单位元的环R上的n阶上三角矩阵环不是半交换环．我们证明了reduced环上的上三角矩阵环的一类特殊子环是半交换环．
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| 关 键 词： | 半交换环 Armendariz环 reduced环 |
| 文章编号： | 1000-341X(2006)02-0264-05 |
| 收稿时间： | 09 13 2004 12:00AM |
| 修稿时间： | 2004年9月13日 |
Semicommutative Subrings of Matrix Rings |
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| LIU Zhong-kui.Semicommutative Subrings of Matrix Rings[J].Journal of Mathematical Research with Applications,2006,26(2):264-268. |
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| Authors: | LIU Zhong-kui |
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| Institution: | Department of Mathematics, Northwest Normal University, Lanzhou 730070, China |
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| Abstract: | A ring $R$ is called semicommutative if for every $a\in R$, $r_R(a)$ is an ideal of $R$. It is well-known that the $n$ by $n$ upper triangular matrix ring is not semicommutative for any ring $R$ with identity when $n\geq 2$. We show that a special subring of upper triangular matrix ring over a reduced ring is semicommutative. |
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| Keywords: | semicommutative ring Armendariz ring reduced ring |
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