Derivations in Hyperrings and Prime Hyperrings

In this paper we introduce derivations in Krasner hyperrings and derive some basic properties of derivations. We also prove that for a strongly differential hyperring $R$ and for any strongly differential hyperideal $I$ of $R,$ the factor hyperring $R/I$ is a strongly differential hyperring. Further we prove that a map $d: R \rightarrow R$ is a derivation of a hyperring $R$ if and only if the induced map $\varphi_d$ is a homomorphism.