Fundamentals of derivations on (ordered) hyper(near)-rings

This paper deals with hyperstructures mainly with (ordered) hyper(near-)rings. In 2013, Asokkumar introduced the concept of derivations on Krasner hyperrings. In the current paper, we introduce and study the concept of derivations on (ordered) hyper(near-)rings. Also, we introduce subhyperrings of the hyperring of \(2 \times 2\) matrices that admit h-derivation with an even degree of nilpotency. Moreover, we prove that some results of derivations on the hyperring of \(2 \times 2\) matrices.