C Jaya’s scientific contributions

... Reverse derivation, generalized reverse derivation, (α, β)-reverse derivation, generalized (α, β)-reverse derivation, multiplicative reverse derivation, multiplicative generalized reverse derivation, multiplicative (α, β)-reverse derivation, and multiplicative generalized (α, β)-reverse derivation of prime or semiprime rings have been studied by a lot of scholars in the literature. (see [2], [3], [4], [9], [10], [12], [13], [14], [15], [16].) This paper extends the notion of one-sided reverse derivation to one-sided generalized (α, β)-reverse derivation. ...

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

... Then it is easy to check that F is a generalized reverse derivation associated with reverse derivation d. For more results concerning reverse derivations and generalized reverse derivations in prime and seiprime rings, we refer the reader to [1] and [16]. ...

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Generalized reverse derivations and commutativity of prime rings

... Molnar [8] studied on centralizers of an H*-algebra. Subba Reddy et al. [9][10][11][12] studied left multiplicative generalized derivations in prime and semiprime rings. Vukman [13] studied a note on generalized derivations of semiprime rings. ...

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Left Multiplicative Generalized Jordan Derivations of Semiprime Rings

... A.H. Majeed [1] explored orthogonal generalized derivations in semiprime -semirings. Recently, C. Jaya Subba Reddy et al. [4,5,6,7] proved some results on the orthogonality of generalized symmetric reverse bi-( , )-derivations in semiprime rings and orthogonality of generalized reverse -(σ,τ)derivations in semiprime Γ-rings. ...

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Orthogonal (𝜎, 𝜏)-Derivations on Semiprime Γ – Semirings

... Relations between derivations and reverse derivations with examples were given by Samman and Alyamani [17]. Recently there has been a great deal of work done by many authors on commutativity and centralizing mappings on prime rings and semi prime rings in connection with derivations, skew derivations, reverse derivations, skew reverse derivations [ 1,[4][5][6][7][8][9][10][11][12][15][16][17][19][20][21][22]. Vukman [19][20][21][22], Mohammad Ashraf [1], Jung and Park [7] have studied the concepts of symmetric biderivations, 3-derivations, 4-derivations and nderivations. ...

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Symmetric Skew Reverse n-Derivations on Prime Rings and Semiprime rings

... In [10] , El-Soufi and Aboubakr proved that J ⊆ Z(R) under specific properties, where R is a 2-torsion free prime ring with center Z(R) admitting a generalized derivation F associated with a derivation d , J is a nonzero Jordan ideal. In addition, Ibraheem in [11] showed that if f is a generalized reverse derivation on R such that f is commuting and centralizing on a right ideal I of R, then R is a commutative, where R is a prime ring and d is a reverse derivation on R. Moreover, in [1], Abu Nawas and Al-Omary investigated the commutativity of R such that R is a * -prime ring admitting generalized (α, β)-derivations F and G associated with (α, β)−derivations d and g, respectively, that satisfying certain properties. ...

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On Ideals and Commutativity of Prime Rings with Generalized Derivations

... To prove that R is Г-regular Let (α ̶ α ω α) ∈ J and there is a unit ω ∈ R * and where α ∈ R such that α ̶ α ω α = (α ̶ α ω α)ߛ(α ̶ α ω α) where ߛ ∈ I * . Then α = α ̶ α ω α + α ω α= (α ̶ α ω α) ߛ (α ̶ α ω α) + α ω α = (α γ⎼ α ω α γ)(α ⎼ α ω α)+ α ω α= α γ α ⎼α γ α ω α ⎼α ω α γ α + α ω α γ α ω α+ α ω α = α(ߛ ̶ ߛ α ω ̶ ω α ߛ ̶ + ω α ߛ α ω + ω)α=α ߜ α, Where ߜ = γ ̶ ߛ α ω ⎼ω α ߛ ̶ + ω α ߛ α ω + ω ∈ R * [11]. Since I * ⊆R * and R * is an ideal in (R, Г).Hence R is Гregular. ...

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The Group Structure of Unit Г-regular Ring Elements