(σ, τ )-Derivation on ordered Γ-semihyperrings

Document Type : Research Paper

Authors

1 Kavayitri Bahinabai Chaudhari North Maharashtra University Jalgaon

2 Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon

Abstract

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

Keywords


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