Geodesic
On Gamma-Rings with $(\sigma,\tau)$-Skew-Commuting and $(\sigma,\tau)$-Skew-Centralizing Mappings
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 1, p. 41 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $M$ be a 2-torsion free $\Gamma$-ring with left identity $e$. Let $D : M x M\rightarrow M$ be a symmetric bi-additive mapping and $d(x) = D(x, x)$. Let $\sigma$ and $\tau$ be an endomorphism and an epimorphism of $M$, respectively. We prove the following: \begin{itemize} em[(i)] if $d$ is $(\sigma ,\tau )$-skew-commuting on $M$, then $D = 0$; em[(ii)] if $d$ is $(\tau ,\tau )$-skew-centralizing on $M$, then $d$ is $(\tau ,\tau )$-commuting on $M$; em[(iii)] if $M$ is a 3-torsion free $\Gamma$-ring satisfying $x\alpha y\beta z=x \beta y \alpha z$ for all $x, y, z\in M$ and $\alpha , \beta \in \Gamma$, then 2-$(\sigma , \tau )$-commutingness of $d$ on $M$ implies its $(\sigma ,\tau )$-commutingness. \end{itemize}
Classification : 16W20 16Y99
Keywords: $\Gamma$-ring, $(\sigma ;\tau )$-skew-commuting mappings, $(\sigma;\tau)$-skew-centralizing mappings, $(\sigma;\tau)$-commuting mappings 
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     author = {Kalyan Kumar Dey and Akhil Chandra Paul and Bijan Davvaz},
     title = {On {Gamma-Rings} with $(\sigma,\tau)${-Skew-Commuting} and $(\sigma,\tau)${-Skew-Centralizing} {Mappings}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {41 },
     publisher = {mathdoc},
     volume = {42},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2018_42_1_a3/}
}
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Kalyan Kumar Dey; Akhil Chandra Paul; Bijan Davvaz. On Gamma-Rings with $(\sigma,\tau)$-Skew-Commuting and $(\sigma,\tau)$-Skew-Centralizing Mappings. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 1, p. 41 . http://geodesic.mathdoc.fr/item/KJM_2018_42_1_a3/