Derivations of the Full Matrix Rings over a Ring
Received:December 19, 1990  
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Deng Qing Dept. of Math.
Southwest China Teachers Univ.
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      Let R be a ring with identity. Let Rn denote the full matrix ring over R and d be a derivation of Rn. In this note, it is shown that each derivation d of Rn may determine a derivation f of R such that d(xE) can be expressed by f for every x in R(E be the unity of Rn). Moreover, the relations between d-and f are discussed. In particulat, a necessary condition for a derivation of R to be extendable to one of Rn's is given.
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