Semi-derivation on prime hyperrings

In this paper, we study the notion of semi-derivation in Krasner hyperring and present some examples of them. We introduce the concept of generalized semi-derivation in Krasner hyperring and present some examples. Then, we derive some properties of semi-derivation on Krasner hyperring which proves the commutativity of a Krasner hyperring. Later we prove if f is a non-zero semi-derivation on Krasner hyperring R, then f۲≠ ۰ on R. Finally, for a generalized semi-derivation F on R, if F(u o v)=۰, for all u,v∈ I, then R is commutative.

Keywords:

Hyperring , hyperideal , derivation , semi-derivation , generalized semi-derivation