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REMARKS ON GENERALIZED (α, β)-DERIVATIONS IN SEMIPRIME RINGS
Hongan, Motoshi,ur Rehman, Nadeem Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.3
Let R be an associative ring and ${\alpha},{\beta}:R{\rightarrow}R$ ring homomorphisms. An additive mapping $d:R{\rightarrow}R$ is called an (${\alpha},{\beta}$)-derivation of R if $d(xy)=d(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for any $x,y{\in}R$, and an additive mapping $D:R{\rightarrow}R$ is called a generalized (${\alpha},{\beta}$)-derivation of R associated with an (${\alpha},{\beta}$)-derivation d if $D(xy)=D(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for all $x,y{\in}R$. In this note, we intend to generalize a theorem of Vukman [5], and a theorem of Daif and El-Sayiad [2].
REMARKS ON GENERALIZED JORDAN (α, β)<sup>*</sup>-DERIVATIONS OF SEMIPRIME RINGS WITH INVOLUTION
Hongan, Motoshi,Rehman, Nadeem ur Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.1
Let R be an associative ring with involution * and ${\alpha},{\beta}:R{\rightarrow}R$ ring homomorphisms. An additive mapping $d:R{\rightarrow}R$ is called an $({\alpha},{\beta})^*$-derivation of R if $d(xy)=d(x){\alpha}(y^*)+{\beta}(x)d(y)$ is fulfilled for any $x,y{\in}R$, and an additive mapping $F:R{\rightarrow}R$ is called a generalized $({\alpha},{\beta})^*$-derivation of R associated with an $({\alpha},{\beta})^*$-derivation d if $F(xy)=F(x){\alpha}(y^*)+{\beta}(x)d(y)$ is fulfilled for all $x,y{\in}R$. In this note, we intend to generalize a theorem of Vukman [12], and a theorem of Daif and El-Sayiad [6], moreover, we generalize a theorem of Ali et al. [4] and a theorem of Huang and Koc [9] related to generalized Jordan triple $({\alpha},{\beta})^*$-derivations.
A NOTE ON MULTIPLICATIVE (GENERALIZED)-DERIVATION IN SEMIPRIME RINGS
REHMAN, NADEEM UR,HONGAN, MOTOSHI The Korean Society for Computational and Applied M 2018 Journal of applied mathematics & informatics Vol.36 No.1
In this article we study two Multiplicative (generalized)- derivations ${\mathcal{G}}$ and ${\mathcal{H}}$ that satisfying certain conditions in semiprime rings and tried to find out some information about the associated maps. Moreover, an example is given to demonstrate that the semiprimeness imposed on the hypothesis of the various results is essential.
A NOTE ON MULTIPLICATIVE (GENERALIZED)-DERIVATION IN SEMIPRIME RINGS
Nadeem Ur Rehman,Motoshi Hongan 한국전산응용수학회 2018 Journal of applied mathematics & informatics Vol.36 No.1
In this article we study two Multiplicative (generalized)- derivations $\mathcal{G}$ and $\mathcal{H}$ that satisfying certain conditions in semiprime rings and tried to find out some information about the associated maps. Moreover, an example is given to demonstrate that the semiprimeness imposed on the hypothesis of the various results is essential.