Biderivations of the Algebra of Strictly Upper Triangular Matrices over a Commutative Ring
Received:April 08, 2010  Revised:May 28, 2010
Key Words: biderivation   strictly upper triangular matrix   algebra.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10971117).
Author NameAffiliation
Pei Seng JI School of Mathematical Sciences, Qingdao University, Shandong 266071, P. R. China 
Xiao Ling YANG School of Mathematical Sciences, Qingdao University, Shandong 26607$, P. R. China 
Jian Hui CHEN School of Mathematical Sciences, Qingdao University, Shandong 266071, P. R. China 
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Abstract:
      Let $N_n(R)$ be the algebra consisting of all strictly upper triangular $n\times n$ matrices over a commutative ring $R$ with the identity. An $R$-bilinear map $\phi :N_n(R)\times N_n(R)\longrightarrow N_n(R)$ is called a biderivation if it is a derivation with respect to both arguments. In this paper, we define the notions of central biderivation and extremal biderivation of $N_n(R)$, and prove that any biderivation of $N_n(R)$ can be decomposed as a sum of an inner biderivation, central biderivation and extremal biderivation for $n\geq 5$.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.06.002
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