On Semigroup Ideals and Generalized $\boldsymbol{n}$-derivations in Near-rings
DOI:
https://doi.org/10.5644/SJM.11.2.02Keywords:
$3$-prime near-ring, semigroup ideals, derivation, $n$-derivation, generalized $n$-derivation and commutativityAbstract
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.
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