ON PRIME AND SEMIPRIME RINGS WITH PERMUTING 3-DERIVATIONS

Title & Authors
ON PRIME AND SEMIPRIME RINGS WITH PERMUTING 3-DERIVATIONS
Jung, Yong-Soo; Park, Kyoo-Hong;

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 $\small{{\Delta}:R{\times}R{\times}R{\rightarrow}R}$ such that the trace is centralizing on I. Then the trace of $\small{{\Delta}}$ is commuting on I. In particular, if R is a 3!-torsion free prime ring and $\small{{\Delta}}$ is nonzero under the same condition, then R is commutative.
Keywords
prime ring;semiprime ring;commuting map;centralizing map;derivation;bi-derivation;3-derivation;
Language
English
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