三角代数上的一类非全局三重可导映射

孟利花, 张建华

数学学报 ›› 2017, Vol. 60 ›› Issue (6) : 955-960.

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PDF(322 KB)
数学学报 ›› 2017, Vol. 60 ›› Issue (6) : 955-960. DOI: 10.12386/A2017sxxb0082
论文

三角代数上的一类非全局三重可导映射

    孟利花, 张建华
作者信息 +

A Class of Non-global Triple Derivable Maps on Triangular Algebras

    Li Hua MENG, Jian Hua ZHANG
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文章历史 +

摘要

T=Tri (A,M,B)为三角代数,Q={TTT2=0}且δTT是一个映射(没有可加或线性假设).证明了:如果对任意A,B,CTABCQ,有δABC)=δABC+AδBC+ABδC),则δ是一个可加导子.作为应用,得到了上三角矩阵代数和套代数上此类非全局三重可导映射的具体形式.

Abstract

Let T=Tri(A, M, B) be a triangular algebra, and Q={TT:T2=0}. We prove that if a map δ:TT satisfies δ(ABC)=δ(A)BC+Aδ(B)C+ABδ(C) for any A, B, CT with ABCQ, then δ is an additive derivation.

关键词

三角代数 / 三重可导映射 / 平方零元

Key words

triangular algebra / triple derivable map / square zero element

引用本文

导出引用
孟利花, 张建华. 三角代数上的一类非全局三重可导映射. 数学学报, 2017, 60(6): 955-960 https://doi.org/10.12386/A2017sxxb0082
Li Hua MENG, Jian Hua ZHANG. A Class of Non-global Triple Derivable Maps on Triangular Algebras. Acta Mathematica Sinica, Chinese Series, 2017, 60(6): 955-960 https://doi.org/10.12386/A2017sxxb0082

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基金

国家自然科学基金资助项目(11471199)

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