Let N be a near ring. An additive mapping f: N→ N is said to be a right generalized (resp., left
generalized) derivation with associated derivation d on N if f (xy)= f (x) y+ xd (y)(resp., f (xy)=
d (x) y+ xf (y)) for all x, y∈ N. A mapping f: N→ N is said to be a generalized derivation with
associated derivation d on N if f is both a right generalized and a left generalized derivation
with associated derivation d on N. 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 …

Let NN be a near ring. An additive mapping f: N ⟶ N f: N⟶ N is said to be a right generalized
(resp. left generalized) derivation with associated derivation dd on NN if f (xy)= f (x) y+ xd (y)
f (xy)= f (x) y+ xd (y)(resp. f (xy)= d (x) y+ xf (y) f (xy)= d (x) y+ xf (y)) for all x, y ∈ N. x, y∈ N. A
mapping f: N ⟶ N f: N⟶ N is said to be a generalized derivation with associated derivation dd
on NN if ff is both a right generalized and a left generalized derivation with associated
derivation dd on N N. The purpose of the present paper is to prove some theorems in the …