On biderivations of upper triangular matrix rings
On biderivations of upper triangular matrix rings
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DOI：
10.1016/j.laa.2012.07.039
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发表时间：
2013
影响因子：
1.1
通讯作者：
Nader M. Ghosseiri
中科院分区：
文献类型：
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作者：
Nader M. Ghosseiri
设R和S是有单位元的环，M是酉型(R，S)-双模，T=RM0S是由R，S和M确定的上三角矩阵环，Eij是标准矩阵单位.本文证明了T的每个双导子都分解为三个双导子D，Ψ和Δ之和，其中D(E11，E11)=0，Ψ是极值双导子，Δ是一种特殊的双导子。利用这个刻划，我们确定了R上所有n×n上三角矩阵的环Tn(R)(n⩾2)的双导子的结构，并证明了当R是非对易素环时，Tn(R)的每个双导子都是内的。这推广了Benkovič(2009年)[1]的一些结果。
Let R and S be rings with identity, M be a unitary (R,S)-bimodule, and T=RM0S be the upper triangular matrix ring determined by R,S and M. Let Eijbe the standard matrix unit. In this paper we show that every biderivation of T is decomposed into the sum of three biderivations D,Ψ and Δ, where D(E11,E11)=0,Ψ is an extremal biderivation and Δ is a special kind of biderivation. Using this characterization, we determine the structure of biderivations of the ring Tn(R)(n⩾2) of all n×n upper triangular matrices over R, and show that in the special case when R is a noncommutative prime ring, every biderivation of Tn(R) is inner. This extends some results of Benkovič (2009) [1].