Some Commutativity Theorems for Prime Near-rings Involving Derivations
Moharram A. Khan *
Department of Mathematics and Computer Science, Faculty of Natural and Applied Sciences, Umaru Musa Yarádua University, Katsina, Katsina State, Nigeria.
Abdu Madugu
Department of Mathematics and Computer Science, Faculty of Natural and Applied Sciences, Umaru Musa Yarádua University, Katsina, Katsina State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The study depicts that a prime near-ring N is considered to be a commutative ring if there non-negative integers exist i.e., 
in such a way that N admits a non-zero derivation, where d satisfying one of the conditions like (C1) - (C8). For any x, y ∈ N , we define the following properties
In addition, an example is given to demonstrate the primeness of the hypothesis which is not superfluous. Finally, we can conclude it with some open problems.
Keywords: Commutativity, derivation, near-ring, prime near-ring, zero-symmetric near-ring.