Geodesic
Generalization of Posner's Theorems
Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 4 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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In this paper we generalize Posner's first theorem to a 3-prime near-ring with a $(\sigma ,\tau )$-derivation. We prove that a prime ring with a non-zero $(\sigma ,\tau )$-derivation is commutative if $\sigma (x)d(x)=d(x)\tau (x)$ for all $x\in U$ where $U$ is a suitable subset of $R$%. Also, we generalize Posner's second theorem completely to a prime ring with a $(\sigma ,\sigma )$-derivation and partially to a prime ring with a $% (\sigma ,\tau )$-derivation.
Classification : 16W25, 16Y30 
@article{BMMS_2013_36_4_a9,
     author = {Ahmed A. M. Kamal and Khalid H. Al-Shaalan}},
     title = {Generalization of {Posner's} {Theorems}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2013},
     volume = {36},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2013_36_4_a9/}
}
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Ahmed A. M. Kamal; Khalid H. Al-Shaalan}. Generalization of Posner's Theorems. Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 4. http://geodesic.mathdoc.fr/item/BMMS_2013_36_4_a9/