### ONE-SIDED GENERALIZED (α, β)−REVERSE DERIVATIONS OF ASSOCIATIVE RINGS

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#### Abstract

In this paper, we introduce the notion of the one-sided generalized (α, β)−reverse

derivation of a ring R. Let R be a semiprime ring, ϱ be a non-zero ideal of R, α be

an epimorphism of ϱ, β be a homomorphism of ϱ (α be a homomorphism of ϱ, β

be an epimorphism of ϱ) and γ : ϱ → R be a non-zero (α, β)−reverse derivation.

We show that there exists F : ϱ → R, an l−generalized (α, β)−reverse derivation

(an r−generalized (α, β)−reverse derivation) associated with γ iff F(ϱ), γ(ϱ) ⊂ CR(ϱ)

and F is an r−generalized (β, α)−derivation (an l−generalized (β, α)−derivation) associated with (β, α)−derivation γ on ϱ. This theorem generalized the results of A.

Aboubakr and S. Gonzalez proved in [1, Theorem 3.1 and Theorem 3.2 ].

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PDF#### References

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DOI: https://doi.org/10.22190/FUMI220322001E

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