Some notes on differential hyperrings

Abstract

In this paper, we introduce the notion of derivation on Krasner hyperrings as follows: the function d : R  R isa derivation on a Krasner hyperring R if for all , , Ry x  ) ( ) ( = ) ( y d x d y x d   andd (x  y) d (x)  y  x  d ( y). Then, we investigate some fundamental properties of derivation on Krasnerhyperings and prime Krasner hyperrings. Also, we introduce differential Krasner hyperingsand discuss some relatedproperties.