(σ, τ)-DERIVATION ON ORDERED Γ-SEMIHYPERRINGS

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Nerkar Lalita Pandurang; Pawar Kishor Fakira

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: Journal of Hyperstructures Year:2023 | Volume:12 | Issue:2 Page(s): 228-243

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Title

(σ, τ)-DERIVATION ON ORDERED Γ-SEMIHYPERRINGS

Author(s)

Nerkar Lalita Pandurang | Pawar Kishor Fakira | Issue Writer Certificate

Keywords

Γ-semihyperring

ordered Γ-semihyperring

(σ

τ)-derivation.

Abstract

When a suitable partial ordered relation is attached to a Γsemihyperring, it results into an ordered Γ-semihyperring. Concepts of an ordered Γ-semihyperring, Γ-band, idempotent Γ-semihyperring, totally ordered Γ-semihyperring, positively ordered Γ-semihyperring, negatively ordered Γ-semihyperring are introduced which are useful to study derivation on ordered Γ-semihyperrings. Derivation is nothing but an additive mapping fulfilling the Leibniz rule. In this paper, we introduce the concept of (σ, τ)-derivation which is a generalization of σ-derivation and derivation 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 encountered.

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