VINCENZO DE FILIPPIS
Derivations on K-th commutators in semiprime rings
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.