Riv.Mat.Univ.Parma (6) 2 (1999)


Derivations on K-th commutators in semiprime rings

Pages: 19-31
Received: 18 January 1999   
Mathematics Subject Classification: 16N60 - 16W25

Abstract: Let R be a 2-torsion free semiprime ring, d a non zero derivation of R and a, b, c, d Î R such that  [d([[a, b], [c, d]]k), [[a, b],[c, d]]k]]¹0. We prove that if [d([[r1 , r2],   [r3 ,r4]] k), [[r1 , r2],  [r3 ,r4 ]]k] is zero or invertible, for any r1 , r2, r3 ,r4 Î R , then R  is a division ring.

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