Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A RESULT ON GENERALIZED DERIVATIONS WITH ENGEL CONDITIONS ON ONE-SIDED IDEALS

  • Demir, Cagri (DEPARTMENT OF MATHEMATICS SCIENCE FACULTY EGE UNIVERSITY) ;
  • Argac, Nurcan (DEPARTMENT OF MATHEMATICS SCIENCE FACULTY EGE UNIVERSITY)
  • Published : 2010.05.01
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Abstract

Let R be a non-commutative prime ring and I a non-zero left ideal of R. Let U be the left Utumi quotient ring of R and C be the center of U and k, m, n, r fixed positive integers. If there exists a generalized derivation g of R such that $[g(x^m)x^n,\;x^r]_k\;=\;0$ for all x $\in$ I, then there exists a $\in$ U such that g(x) = xa for all x $\in$ R except when $R\;{\cong}\;=M_2$(GF(2)) and I[I, I] = 0.

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References

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