| 关于斜McCoy环 |
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| 引用本文： | 宋雪梅,李旭东,杨世洲.关于斜McCoy环[J].数学研究及应用,2011,31(2):323-329. |
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| 作者姓名： | 宋雪梅 李旭东 杨世洲 |
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| 作者单位： | 兰州城市学院数学学院, 甘肃 兰州 730070;兰州城市学院数学学院, 甘肃 兰州 730070;西北师范大学数学与信息科学学院, 甘肃 兰州 730070 |
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| 基金项目： | 甘肃省自然科学基金 (Grant No.3ZS061-A25-015), 甘肃省教育厅科技基金 (Grant No.06021-21). |
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| 摘 要： | For a ring endomorphism α,we introduce α-skew McCoy rings which are generalizations of α-rigid rings and McCoy rings,and investigate their properties.We show that if α t = I R for some positive integer t and R is an α-skew McCoy ring,then the skew polynomial ring Rx;α] is α-skew McCoy.We also prove that if α（1） = 1 and R is α-rigid,then Rx;α]/ x 2 is αˉ-skew McCoy.
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| 关 键 词： | McCoy ring skew McCoy ring skew polynomial ring rigid ring skew Armendariz ring upper triangular matrix ring |
| 收稿时间： | 2009/1/18 0:00:00 |
| 修稿时间： | 2010/1/19 0:00:00 |
On Skew McCoy Rings |
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| Xue Mei SONG,Xu Dong LI and Shi Zhou YANG.On Skew McCoy Rings[J].Journal of Mathematical Research with Applications,2011,31(2):323-329. |
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| Authors: | Xue Mei SONG Xu Dong LI and Shi Zhou YANG |
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| Institution: | 1. College of Mathematics, Lanzhou City University, Gansu 730070, P. R. China
2. College of Mathematics and Information Science, Northwest Normal University, Gansu 730070, P. R. China |
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| Abstract: | For a ring endomorphism $\alpha$, we introduce $\alpha$-skew McCoy rings which are generalizations of $\alpha$-rigid rings and McCoy rings, and investigate their properties. We show that if $\alpha^t=I_R$ for some positive integer $t$ and $R$ is an $\alpha$-skew McCoy ring, then the skew polynomial ring $Rx;\alpha]$ is $\alpha$-skew McCoy. We also prove that if $\alpha(1)=1$ and $R$ is $\alpha$-rigid, then $Rx;\alpha]/\langle x^2\rangle$ is $\bar{\alpha}$-skew McCoy. |
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| Keywords: | McCoy ring skew McCoy ring skew polynomial ring rigid ring skew Armendariz ring upper triangular matrix ring |
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