Semi-derivation on prime hyperrings - Nikhil D. Sonone; Kishor F. Pawar (Journal of Hyperstructures)
In this paper, we study the notion of semi-derivation in Krasner hyperring and present some examples of them.We intro-duce the concept of generalized semi-derivation in Krasner hyper-ring and present some examples.Then, we derive some properties of semi-derivation on Krasner hyperring which proves the commu-tativity of a Krasner hyperring. Later we prove if f is a non-zero semi-derivation on Krasner hyperring R, then f2≠ 0 on R. Finally, for a generalized semi-derivation F on R, if F(u o v)=0, for all u,v∈ I, then R is commutative.