Derivations on Semiprime Rings and Banach Algebras, I

  • Kim, Byung-Do (Department of Mathematics Kangnung National University) ;
  • Lee, Yang-Hi (Department of Mathematics Education Kongju National Teacher's College)
  • 투고 : 1994.06.30
  • 발행 : 1994.06.30

초록

The aim of this paper is to give the partial answer of Vukman's conjecture [2]. From the partial answer we also generalize a classical result of Posner. We prove the following result: Let R be a prime ring with char$(R){\neq}2,3$, and 5. Suppose there exists a nonzero derivation $D:R{\rightarrow}R$ such that the mapping $x{\longmapsto}$ [[[Dx,x],x],x] is centralizing on R. Then R is commutative. Using this result and some results of Sinclair and Johnson, we generalize Yood's noncom-mutative extension of the Singer-Wermer theorem.

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