Derivations of gamma (semi)hyperrings

Abstract

Differential $\Gamma$ -(semi)hyperrings are $\Gamma$ -(semi)hyperrings equipped with derivation, which is a linear unary function satisfying the Leibniz product rule.We introduce the notions of derivation and weak derivation on $\Gamma$ -hyperrings and $\Gamma$ -semihyperrings and obtain some important results relating to them in a specific way.