Generalized Derivations on Prime Near Rings
Let be a near ring. An additive mapping is said to be a
right generalized (resp., left generalized) derivation with associated derivation on if (resp., ) for all . A mapping
 is said to be a generalized derivation with associated derivation on if
 is both a right generalized and a left generalized derivation with associated derivation
 on . The purpose of the present paper is to prove some theorems in the setting of
a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby
extending some known results on derivations.
• A PAIR OF GENERALIZED (σ,τ) n-DERIVATIONS IN PRIME NEAR RINGS
T he purpose of this paper is to study generalized derivations satisfying certain identities on semigroup ideals of a prime near ring. Some well known results characterizing commutativity of 3-prime near rings by -derivations have been generalized using semigroup ideals.
ON PERMUTING n-DERIVATIONS IN NEAR-RINGS
In this paper, we introduce the notion of permuting n-deri- vations in near-ring N and investigate commutativity of addition and multiplication of N. Further, under certain constrants on a n!-torsion free prime near-ring N, it is shown that a permuting n-additive mapping D on N is zero if the trace d of D is zero. Finally, some more related results are also obtained.