On prime and semiprime rings with permuting 3-derivations
Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 789-794
Published online December 1, 2007
Yong-Soo Jung and Kyoo-Hong Park
Sun Moon University, Seowon University
Abstract : Let $R$ be a $3$-torsion free semiprime ring and let $I$ be a nonzero two-sided ideal of $R$. Suppose that there exists a permuting 3-derivation $\D : R\times R\times R \to R$ such that the trace is centralizing on $I$. Then the trace of $\D$ is commuting on $I$. In particular, if $R$ is a $3!$-torsion free prime ring and $\D$ is nonzero under the same condition, then $R$ is commutative.
Keywords : prime ring, semiprime ring, commuting map, centralizing map, derivation, bi-derivation, 3-derivation
MSC numbers : 16W20, 16W25
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