三角代数上的非线性(m,n)-高阶导子

费秀海, 张建华, 王中华

数学学报 ›› 2016, Vol. 59 ›› Issue (5) : 645-658.

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数学学报 ›› 2016, Vol. 59 ›› Issue (5) : 645-658. DOI: 10.12386/A2016sxxb0059
论文

三角代数上的非线性(m,n)-高阶导子

    费秀海, 张建华, 王中华
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Nonlinear (m,n)-Higher Derivations On Triangular Algebras

    Xiu Hai FEI, Jian Hua ZHANG, Zhong Hua WANG
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文章历史 +

摘要

mn是任意固定的非零整数且(m+n)(m-n)≠0,U是一个|mnm+n)|-无挠的三角代数,D={dk}k∈N是U上的一个(mn)-高阶可导映射.本文证明了:三角代数U上的每一个(mn)-高阶可导映射都是高阶导子.作为结论的应用,得到了套代数或|mnm+n)|-无挠的上三角分块矩阵代数上的每一个(mn)-高阶可导映射都是高阶导子.

Abstract

Let m,n be non-zero integers with (m+n)(m-n)≠0, U an|mn(m+n)|-torsion free triangular algebra and D={dk}k∈N (m,n)-higher derivable map from U into itself. In this paper, it is shown that every (m,n)-higher derivable map on U is a higher derivation. As its application, we get that every (m,n)-higher derivable map on a nest algebra or an|mn(m+n)|-torsion free block upper triangular matrix algebra is a higher derivation.

关键词

三角代数 / (m / n)-导子 / (m / n)-高阶导子

Key words

Triangular algebra / (m,n)-derivation / (m,n)-higher derivation

引用本文

导出引用
费秀海, 张建华, 王中华. 三角代数上的非线性(m,n)-高阶导子. 数学学报, 2016, 59(5): 645-658 https://doi.org/10.12386/A2016sxxb0059
Xiu Hai FEI, Jian Hua ZHANG, Zhong Hua WANG. Nonlinear (m,n)-Higher Derivations On Triangular Algebras. Acta Mathematica Sinica, Chinese Series, 2016, 59(5): 645-658 https://doi.org/10.12386/A2016sxxb0059

参考文献

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基金

国家自然科学基金项目(11371233,11471199);博士学科点专项科研基金(20110202110002)

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