Some notes on differential hyperrings

In this paper, we introduce the notion of derivation on Krasner hyperrings as follows: the function d :R?R is a derivation on a Krasner hyperring R if for all x, y?R, d(x? y) = d(x)?d(y) and d(x ? y)?d(x) ? y ? x ?d(y). Then, we investigate some fundamental properties of derivation on Krasner hyperings and prime Krasner hyperrings. Also, we introduce differential Krasner hyperingsand discuss some related properties.