On Semigroup Ideals and Right n-Derivation in 3-Prime Near-Rings

The current paper studied the concept of right n-derivation satisfying certified conditions on semigroup ideals near-rings and some related properties. Interesting results have been reached, most prominent which are following: Let M be a 3-prime left near-ring A_1,A_2,…,A_n nonzero M, if d is satisfies following conditions,d(u_1,u_2,…,(u_j,v_j ),…,u_n )=0 ∀ 〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n ϵA〗_u;d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=0 ∀u_1,v_1 〖ϵA〗_1,u_2,v_2 A_j,…,〖u_n,v_n ϵA〗_u ;d((u_1,v_1 ))=(u_j,v_j ) u_1,v_1 ,u_2,v_2 ϵA〗_u;If d+d an n -additive mapping from A_1×A_2×…×A_n to M;d(u_1,u_2,…,(u_j,v_j ),…,u_n)∈ Z(M) ∀〖 ϵA〗_u,; d((u_1,v_1 ))∈ ϵA〗_u;Then commutative ring.