DERIVATIONS OF PRIME AND SEMIPRIME RINGS

Title & Authors
DERIVATIONS OF PRIME AND SEMIPRIME RINGS
Argac, Nurcan; Inceboz, Hulya G.;

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+$\small{yd(x))^n}$ = xy + yx for all x, y $\small{\in}$ I, then R is commutative. (ii) If char R $\small{\neq}$ = 2 and (d(x)y + xd(y) + d(y)x + $\small{yd(x))^n}$ - (xy + yx) is central for all x, y $\small{\in}$ 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;
Language
English
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