ON PRIME AND SEMIPRIME RINGS WITH PERMUTING 3-DERIVATIONS

Jung, Yong-Soo; Park, Kyoo-Hong

doi:10.4134/BKMS.2007.44.4.789

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ON PRIME AND SEMIPRIME RINGS WITH PERMUTING 3-DERIVATIONS

Journal title : Bulletin of the Korean Mathematical Society
Volume 44, Issue 4, 2007, pp.789-794
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2007.44.4.789

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 ${${\Delta}:R{\times}R{\times}R{\rightarrow}R$}$ such that the trace is centralizing on I. Then the trace of ${${\Delta}$}$ is commuting on I. In particular, if R is a 3!-torsion free prime ring and ${${\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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