Title
kDerivations and kHomomorphisms of Gamma Rings: Jordan kDerivations, Jordan Left/Right and Generalized kDerivations, Jordan ,Used
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The notion of a gamma ring is a generalization of the concept of a classical ring. This attempt characterizes certain gamma rings with various types of kderivations and khomomorphisms. We determine the commutativity of prime gamma rings of characteristic not equal to 2 and 3 with kderivations, left (and right) kderivations and generalized kderivations. We prove that every Jordan kderivation (also, Jordan generalized kderivation) of a gamma ring is a kderivation (generalized kderivation) of the same, if we consider the gamma ring as a (2torsion free) prime, completely prime, semiprime, and completely semiprime gamma ring, under some suitable conditions (as necessary), respectively. On the other hand, we prove that every Jordan khomomorphism of a gamma ring onto a 2torsion free prime (also, completely prime) gamma ring is either a khomomorphism or an antikhomomorphism. The analogous result is also proved for Jordan kisomorphism of a gamma ring onto a 2torsion free prime/completely prime gamma ring. Finally, we investigate what does happen if a kderivation acts as a kendomorphism and also as an antikendomorphism of certain gamma rings and look what we have here.
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