On Semigroup Ideals and Generalized $\boldsymbol{n}$-derivations in Near-rings - Ashraf, Mohammad; Siddeeque, Mohammad Aslam (Sarajevo Journal of Mathematics, 2024)
In the present paper, we investigate the commutativity of addition and ring behavior of $3$-prime near-rings satisfying certain conditions involving generalized $n$-derivations on semigroup ideals. Moreover, examples justifying the necessity of the $3$-primeness condition in all the results are provided.