COMMUTATIVITY OF NEAR RINGS WITH GENERALIZED DERIVATIONS

Abstract

The main objective of this project work was to discuss the commutativity conditions of near rings involving generalized derivations. In algebra, there are several conditions that can be used to show the prime near rings are commutative rings. In general, not every near ring is ring by its algebraic structure, but by using generalized derivations of near rings, it is conceivable to extend a prime near ring to commutative ring. For this, we discussed different conditions in different theorems and also we provided the detail proofs of the theorems concerning with generalized derivations. In each of the theorem we discussed different lemmas and some of the related concepts were used to show a given near ring is a commutative ring. Other properties of generalized derivations on near rings such as homomorphism and anti-homomorphism were discussed. Illustrative examples were presented to clarify more concepts and to show the necessity of primeness in the theorems we deal