| 可换环上上三角矩阵代数的局部若当导子和局部若当自同构 |
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| 引用本文： | 赵延霞,姚瑞平,王登银.可换环上上三角矩阵代数的局部若当导子和局部若当自同构[J].数学研究及应用,2010,30(3):465-474. |
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| 作者姓名： | 赵延霞 姚瑞平 王登银 |
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| 作者单位： | 河南理工大学数学与信息科学学院, 河南 焦作 454000;中国矿业大学理学院, 江苏 徐州 221008;中国矿业大学理学院, 江苏 徐州 221008 |
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| 基金项目： | 河南理工大学博士基金（Grant No.B2010-93） |
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| 摘 要： | Let R be a commutative ring with identity, Tn （R） the R-algebra of all upper triangular n by n matrices over R. In this paper, it is proved that every local Jordan derivation of Tn （R） is an inner derivation and that every local Jordan automorphism of Tn（R） is a Jordan automorphism. As applications, we show that local derivations and local automorphisms of Tn （R） are inner.
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| 关 键 词： | Keywords local Jordan derivations local Jordan automorphisms local derivations localautomorphisms upper triangular matrix algebras. |
| 收稿时间： | 2008/3/12 0:00:00 |
| 修稿时间： | 1/5/2009 12:00:00 AM |
Local Jordan Derivations and Local Jordan Automorphisms of Upper Triangular Matrix Algebras |
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| Yan Xia ZHAO,Rui Ping YAO and Deng Yin WANG.Local Jordan Derivations and Local Jordan Automorphisms of Upper Triangular Matrix Algebras[J].Journal of Mathematical Research with Applications,2010,30(3):465-474. |
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| Authors: | Yan Xia ZHAO Rui Ping YAO and Deng Yin WANG |
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| Institution: | 1. School of Mathematics and Information Science, Henan Polytechnic University,Henan 454000, P. R. China
2. Department of Mathematics, China University of Mining and Technology,Jiangsu 221008, P. R. China |
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| Abstract: | Let $R$ be a commutative ring with identity, $T_{n}(R)$ the $R$-algebra of all upper triangular $n$ by $n$ matrices over $R$. In this paper, it is proved that every local Jordan derivation of $T_{n}(R)$ is an inner derivation and that every local Jordan automorphism of $T_{n}(R)$ is a Jordan automorphism. As applications, we show that local derivations and local automorphisms of $T_{n}(R)$ are inner. |
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| Keywords: | local Jordan derivations local Jordan automorphisms local derivations local automorphisms upper triangular matrix algebras |
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