Derivations and Centroids of Four Dimensional Associative Algebras
  In this paper, we focus on derivations and centroids of four dimensional associative algebras. Using an existing classification result of low dimensional associative algebras, we describe the derivations and centroids of four dimensional associative algebras. We also identify algebra(s) that belong to the characteristically nilpotent class among the algebras of four dimensional associative algebras. 
A.O. Abdulkareem, M.A. Fiidow and I.S. Rakhimov
math.RA