| 三角矩阵代数上的保交换可加映射 |
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| 引用本文： | 李晋秀.三角矩阵代数上的保交换可加映射[J].数学杂志,2004,24(2):134-138. |
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| 作者姓名： | 李晋秀 |
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| 作者单位： | 东华大学应用数学系,上海,200051 |
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| 基金项目： | SupportedbytheNSFofShanghaiScienceandTechnologyCommission(No .0 1ZA1 4 0 0 3.) |
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| 摘 要： | 本文研究了三角矩阵代数上保持交换性的可加映射的结构.利用最近Marcoux与Sourour发表在Linear
Alg.Appl.288(1999),89-104]上的一个结果,我们证明了任意域F上的三角矩阵代数Tn(F)(n＞2)上的可加满射ψ双向保交换当且仅当ψ是Tn(F)上一个可加泛函与Tn(F)上某个环自同构或环反自同构之和.
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| 关 键 词： | 三角矩阵代数 可加映射 保交换性映射 |
ADDITIVE COMMUTATIVITY PRESERVING MAPPINGS ON TRIANGULAR MATRIX ALGEBRAS |
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| Abstract.ADDITIVE COMMUTATIVITY PRESERVING MAPPINGS ON TRIANGULAR MATRIX ALGEBRAS[J].Journal of Mathematics,2004,24(2):134-138. |
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| Authors: | Abstract |
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| Abstract: | We study in this paper the structure of additive mappings on triangular matrix algebras which preserve commutativity. By using a recent result of Marcoux and Sourour Linear Alg. Appl. , 288(1999) ,89-104] we show that an additive surjective mapping ψ on the triangular matrix algebra Tn (F) (n＞2) over an arbitrary field F preserves commutativity in both directions if and only if ψ is the sum of an additive functional on Tn(F) with either a certain ring automorphism or a certain ring anti-automorphism of Tn (F) |
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| Keywords: | triangular matrix algebra additive mapping commutativity preserver |
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