| 矩阵环中的一类极大的广义的Armendariz子环 |
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| 引用本文： | 王文康. 矩阵环中的一类极大的广义的Armendariz子环[J]. 数学研究及应用, 2009, 29(1): 185-190 |
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| 作者姓名： | 王文康 |
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| 作者单位： | 西北民族大学计算机科学与信息工程学院, 甘肃 兰州 730124 |
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| 摘 要： | An associative ring with identity R is called Armendariz if, whenever （∑^m i=0^aix^i）（∑^n j=0^bjx^j）=0 in R[x],aibj=0 for all i and j. An associative ring with identity is called reduced if it has no non-zero nilpotent elements. In this paper, we define a general reduced ring （with or without identity） and a general Armendariz ring （with or without identity）, and identify a class of maximal general Armendariz subrings of matrix rings over general reduced rings.
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| 关 键 词： | 环论 抽象代数 代数学 研究 |
| 收稿时间： | 2006-11-11 |
| 修稿时间： | 2007-10-28 |
A Class of Maximal General Armendariz Subrings of Matrix Rings |
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| WANG Wen Kang. A Class of Maximal General Armendariz Subrings of Matrix Rings[J]. Journal of Mathematical Research with Applications, 2009, 29(1): 185-190 |
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| Authors: | WANG Wen Kang |
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| Affiliation: | School of Computer Science and Information Engineering, Northwest University for Nationalities, Gansu 730124, China |
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| Abstract: | An associative ring with identity $R$ is called Armendariz if, whenever $(sum_{i=0}^{m}a_{i}x^{i})$ $(sum_{j=0}^{n}b_{j}x^{j})=0$ in $R[x]$, $a_{i}b_{j}=0$ for all $i$ and $j$. An associative ring with identity is called reduced if it has no non-zero nilpotent elements. In this paper, we define a general reduced ring (with or without identity) and a general Armendariz ring (with or without identity), and identify a class of maximal general Armendariz subrings of matrix rings over general reduced rings. |
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| Keywords: | general Armendariz ring matrix ring general reduced ring. |
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