Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지

ON PRIME AND SEMIPRIME RINGS WITH SYMMETRIC n-DERIVATIONS

  • Received : 2009.05.29
  • Accepted : 2009.08.14
  • Published : 2009.09.30
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Abstract

Let $n{\geq}2$ be a fixed positive integer and let R be a noncommutative n!-torsion free semiprime ring. Suppose that there exists a symmetric n-derivation $\Delta$ : $R^{n}{\rightarrow}R$ such that the trace of $\Delta$ is centralizing on R. Then the trace is commuting on R. If R is a n!-torsion free prime ring and $\Delta{\neq}0$ under the same condition. Then R is commutative.

Keywords

References

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