DERIVATIONS OF PRIME AND SEMIPRIME RINGS
Makaleler > Tam Makale · 2009
Yazarlar: Nurcan Argac, Hulya G. Inceboz
Journal of the Korean Mathematical Society, Uluslararası, Wos, 2009, cilt 46, ss 997-1005
DOI: 10.4134/jkms.2009.46.5.997
Özet
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.