Generalized Derivations Acting as Homomorphisms and Anti-Homomorphisms of Gamma Rings
Keywords:Prime Gamma-rings, generalized derivations, torsion free Gamma-rings, homomorphisms and anti-homomorphisms.
Let M be a prime G-ring and let I be a nonzero ideal of M. Suppose that D: M ® M is a nonzero generalized derivation with associated derivation d : M ® M. Then we prove the following:
(i) If D acts as a homomorphism on I, then either d = 0 on M or M is commutative.
(ii) If M satisfies the assumption (*) (see below), and if D acts as an anti-homomorphism on I, then either d = 0 on M or M is commutative.
Keywords: Prime G-rings; Generalized derivations; Torsion free G-rings; Homomorphisms; Anti-homomorphisms.
© 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.
J. Sci. Res. 4 (1), 33-37 (2012)
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