| 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 |
| 矩阵环的半交换子环 |
| Semicommutative Subrings of Matrix Rings |
| 投稿时间：2004-09-13 |
| DOI：10.3770/j.issn:1000-341X.2006.02.011 |
| 中文关键词: 半交换环 Armendariz环 reduced环. |
| 英文关键词:semicommutative ring Armendariz ring reduced ring. |
| 基金项目:国家自然科学基金 (10171082) |
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| 中文摘要: |
| 称环$R$是半交换的,如果对任意$a\in R, r_R(a)$是$R$的理想.若$n\ge 2$, 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. |
| 英文摘要: |
| 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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