(σ, τ )-derivation on ordered γ-semihyperrings

When a suitable partial ordered relation is attached to a gamma;-semihyperring, it results into an ordered gamma;-semihyperring. concepts of an ordered gamma;-semihyperring, gamma;-band, idempotent gamma;-semihyperring, totally or-dered gamma;-semihyperring, positively ordered gamma;-semihyperring, negatively or-dered gamma;-semihyperring are introduced which are useful to study derivation on ordered gamma;-semihyperrings. derivation is nothing but an additive map-ping fulfilling the leibniz rule. in this paper, we introduce the concept of ( sigma;, tau;)-derivation which is a generalization of sigma;-derivation and deriva-tion on gamma;-semihyperring and study some properties of ( sigma;, tau;)-derivation on an ordered gamma;-semihyperring. some results reflecting different natures of ( sigma;, tau;)-derivation depending on natures of the endomorphisms are encoun-tere