Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DERIVATIONS OF PRIME AND SEMIPRIME RINGS

  • Argac, Nurcan (DEPARTMENT OF MATHEMATICS SCIENCE FACULTY EGE UNIVERSITY) ;
  • Inceboz, Hulya G. (DEPARTMENT OF MATHEMATICS SCIENCE AND ART FACULTY ADNAN MENDERES UNIVERSITY)
  • Published : 2009.09.01
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Abstract

Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and n a fixed positive integer. (i) If (d(x)y+xd(y)+d(y)x+$yd(x))^n$ = xy + yx for all x, y $\in$ I, then R is commutative. (ii) If char R $\neq$ = 2 and (d(x)y + xd(y) + d(y)x + $yd(x))^n$ - (xy + yx) is central for all x, y $\in$ I, then R is commutative. We also examine the case where R is a semiprime ring.

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References

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