대한수학회지 (Journal of the Korean Mathematical Society)

  • 제47권3호
  • /
  • Pages.483-494
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  • 2010
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 발행 : 2010.05.01
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초록

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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참고문헌

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피인용 문헌

  1. A Characterization of Generalized Derivations on Prime Rings vol.44, pp.8, 2016, https://doi.org/10.1080/00927872.2015.1065861
  2. Hypercentralizing generalized skew derivations on left ideals in prime rings vol.173, pp.3, 2014, https://doi.org/10.1007/s00605-013-0486-1