Research Projects

The main object of the proposed work is to study some functional identities involving generalized derivations, generalized (α, β)-derivations, b-generalized skew-derivations and b-generalized (α, β)-derivations in prime rings and then to determine the structure of ring and the associated maps. A functional identity (FI) satisfied by a ring R means an identical relation involving arbitrary elements in R with some unknown maps of R. The usual goal when considering these identities is to describe the form of the mappings appearing in the identity. When this is not possible, then we determine the structure of the ring admitting this identity. The following mappings are to be considered under this project: • generalized derivations, • generalized (α, β)-derivations, • b-generalized skew-derivations • b-generalized (α, β)-derivations, and • some related additive maps. Attempt are to be taken to solve some existing problems.