Glasnik Matematicki, Vol. 39, No.1 (2004), 27-30.
ON GENERALIZED DERIVATIONS AS HOMOMORPHISMS
Department of Mathematics, Birla Institute of Technology and Science,
Pilani 333031, Rajasthan, India
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)
for all x,y ∈
I, then R is commutative.
2000 Mathematics Subject Classification.
16W25, 16N60, 16U80.
Key words and phrases. Prime rings, generalized
derivations, torsion free rings, homomorphisms and anti-homomorphisms.
Full text (PDF) (free access)
Glasnik Matematicki Home Page