The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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HIGHER LEFT DERIVATIONS ON SEMIPRIME RINGS

  • Received : 2010.07.27
  • Accepted : 2010.11.19
  • Published : 2010.11.30
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Abstract

In this note, we extend the Bresar and Vukman's result [1, Proposition 1.6], which is well-known, to higher left derivations as follows: let R be a ring. (i) Under a certain condition, the existence of a nonzero higher left derivation implies that R is commutative. (ii) if R is semiprime, every higher left derivation on R is a higher derivation which maps R into its center.

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References

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