Derivations in Hyperrings and Prime Hyperrings

Abstract

In this paper we introduce derivations in Krasner hyperrings and derive some basic properties of derivations. We also prove that for a strongly dierential hyperring R and for any strongly dierential hyper- ideal I of R, the factor hyperring R/I is a strongly dierential hyperring. Further we prove that a map d : R ! R is a derivation of a hyperring R if and only if the induced map 'd is a homomorphism.