# ON PRIME AND SEMIPRIME RINGS WITH PERMUTING 3-DERIVATIONS

• 발행 : 2007.11.30

#### 초록

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.

#### 참고문헌

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#### 피인용 문헌

1. On Skew Centralizing Traces of Permuting n-Additive Mappings vol.55, pp.1, 2015, https://doi.org/10.5666/KMJ.2015.55.1.1
2. n -Derivations of triangular algebras vol.439, pp.2, 2013, https://doi.org/10.1016/j.laa.2013.03.032
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