| 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. DOI: 10.3770/j.issn:1000-341X.2011.02.016 |
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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 R[x;α] is α-skew McCoy.We also prove that if α（1） = 1 and R is α-rigid,then R[x;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： | 2009-01-18 |
| 修稿时间： | 2010-01-19 |
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. DOI: 10.3770/j.issn:1000-341X.2011.02.016 |
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| Authors: | Xue Mei SONG Xu Dong LI Shi Zhou YANG |
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| Affiliation: | 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 $R[x;alpha]$ is $alpha$-skew McCoy. We also prove that if $alpha(1)=1$ and $R$ is $alpha$-rigid, then $R[x;alpha]/langle x^2rangle$ 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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