Outer derivations of low-dimensional diassociative algebras

The work of outer derivations is extremely extensive research that occurs in many sorts of mathematics fields. This work is concerned with the description of outer derivation for diassociative algebras which is isomorphic to the first cohomology group. The inner derivation (resp. the derivation) interpreted as 1-coboundaries (resp. 1-cocycles). In this regard, we propose an algebraic method to get an important specific case of derivations, known as inner derivation. The procedure is used to determine the inner derivatives of diassociative algebras.