(s ;t )-Derivation on ordered G-semihyperrings

When a suitable partial ordered relation is attached to a G-semihyperring, it results into an ordered G-semihyperring. Concepts of an ordered G-semihyperring, G-band, idempotent G-semihyperring, totally ordered G-semihyperring, positively ordered G-semihyperring, negatively ordered G-semihyperring are introduced which are useful to study derivation on ordered G-semihyperrings. Derivation is nothing but an additive mapping fulfilling the Leibniz rule. In this paper, we introduce the concept of (s ;t )-derivation which is a generalization of s -derivation and derivation on G-semihyperring and study some properties of (s ;t )-derivation on an ordered G-semihyperring. Some results reflecting different natures of (s ;t )-derivation depending on natures of the endomorphisms are encountered.