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http://dx.doi.org/10.4134/JKMS.2009.46.5.997

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)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.5, 2009 , pp. 997-1005 More about this Journal
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.
Keywords
prime and semiprime rings; left Utumi quotient rings; differential identities; derivations;
Citations & Related Records

Times Cited By Web Of Science : 2  (Related Records In Web of Science)
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