Local Derivations of a Matrix Algebra over a Commutative Ring
Received:January 19, 2010  Revised:October 08, 2010
Key Word: derivations   local derivations   $R$-algebras.
Fund ProjectL:Supported by the K.C. Wang Education Foundation of Hong Kong.
 Author Name Affiliation Xian WANG Department of Mathematics, China University of Mining and Technology, Jiangsu 221008, P. R. China
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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 $R$. Several types of proper local derivations of $N_n(R)~(n\leq 4)$ are constructed, based on which all local derivations of $N_n(R)~(n\leq 4)$ are characterized when $R$ is a domain.