SZDerivations, PZDerivations and SDerivations of a Matrix Algebra over Commutative Rings 
Received:March 18, 2008 Revised:July 07, 2008 
Key Words:
SZderivations Sderivations PZderivations.

Fund Project:Fond of China University of Mining and Technology. 

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Abstract: 
Let $R$ be a commutative ring with identity, $N_n(R)$ the matrix algebra consisting of all $n\times n$ strictly upper triangular matrices over $R$ with the usual product operation. An $R$linear map $\phi: N_n(R)\to N_n(R) $ is said to be an SZderivation of $N_n(R)$ if $x^2=0$ implies that $\phi(x)x x\phi(x)=0$. It is said to be an Sderivation of $N_n(R)$ if $\phi(x^2)=\phi(x)x x\phi(x)$ for any $x\in N_n(R)$. It is said to be a PZderivation of $N_n(R)$ if $xy=0$ implies that $\phi(x)y x\phi(y)=0$. In this paper, by constructing several types of standard SZderivations of $N_n(R)$, we first characterize all SZderivations of $N_n(R)$. Then, as its application, we determine all Sderivations and PZderivations of $N_n(R)$, respectively. 
Citation: 
DOI:10.3770/j.issn:1000341X.2009.06.005 
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