Derivations, Centroids and Iner-Derivations of $\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras

This study focuses on the analysis of derivations, centroids, and inner derivations of 5-dimensional complex nilpotent associative algebras. It presents the classification of these algebras of dimension less than five, as well as the classifications of their corresponding derivations, centroids and iner-derivations.