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ON PRIME AND SEMIPRIME RINGS WITH PERMUTING 3-DERIVATIONS

  • Jung, Yong-Soo (DEPARTMENT OF MATHEMATICS SUN MOON UNIVERSITY) ;
  • Park, Kyoo-Hong (DEPARTMENT OF MATHEMATICS EDUCATION SEOWON UNIVERSITY)
  • Published : 2007.11.30

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

References

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  3. Prime and semiprime rings with symmetric skew 3-derivations vol.87, pp.1-2, 2014, https://doi.org/10.1007/s00010-013-0208-8
  4. PAIR OF (GENERALIZED-)DERIVATIONS ON RINGS AND BANACH ALGEBRAS vol.46, pp.5, 2009, https://doi.org/10.4134/BKMS.2009.46.5.857
  5. SKEW n-DERIVATIONS ON SEMIPRIME RINGS vol.50, pp.6, 2013, https://doi.org/10.4134/BKMS.2013.50.6.1863
  6. ON PERMUTING 3-DERIVATIONS AND COMMUTATIVITY IN PRIME NEAR-RINGS vol.25, pp.1, 2010, https://doi.org/10.4134/CKMS.2010.25.1.001
  7. Derivation-homomorphisms vol.40, pp.13036149, 2016, https://doi.org/10.3906/mat-1505-55