Glasnik matematički, Vol. 39 No. 1, 2004.
Original scientific paper
On generalized derivations as homomorphisms and anti-homomorphisms
Nadeem-úr Rehman
Abstract
The concept of derivations as well as generalized derivations (i.e. Ia,b(x) = ax + xb, for all a,b R) have been generalized as an additive function F : R R satisfying F(xy) = F(x)y + xd(y) for all x,y R, where d is a nonzero derivation on R. Such a function F is said to be a generalized derivation. In the present paper it is shown that: if R is 2-torsion free prime ring, I 0 an ideal of R and F a generalized derivation of R such that either F(xy) = F(x)F(y) or F(xy) = F(y)F(x) for all x,y I, then R is commutative.
Keywords
Prime rings; generalized derivations; torsion free rings; homomorphisms and anti-homomorphisms
Hrčak ID:
1260
URI
Publication date:
1.6.2004.
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