Derivations of the Full Matrix Rings over a Ring

Abstract:

      Let R be a ring with identity. Let R_n denote the full matrix ring over R and d be a derivation of R_n. In this note, it is shown that each derivation d of R_n 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 R_n). 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 R_n's is given.