Geodesic
Some Results for Endomorphisms in Prime Rings
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 6, p. 943

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

In this article, we present some commutativity theorems for a prime ring $\mathcal{R}$ equipped with endomorphisms $\alpha$, $\beta$, $\gamma$ and $\delta$ satisfying any one of the following identities: \begin{enumerate} em[(1)] $\:[\alpha(x), \beta(y)]+\gamma([x, y])+\delta(x\circ y)=0$ for all $x, y\in \mathcal{R};$ em[(2)] $\:\alpha(x)\circ \beta(y)+\gamma([x, y])=0$ for all $x, y\in \mathcal{R}$. \end{enumerate} Moreover, we provide examples to show that the assumed restrictions cannot be relaxed.
Classification : 16N60, 15A27, 16S50
Keywords: prime ring, endomorphisms, commutativity 
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     author = {Abdelkarim Boua},
     title = {Some {Results} for {Endomorphisms} in {Prime} {Rings}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {943 },
     publisher = {mathdoc},
     volume = {45},
     number = {6},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2021_45_6_a7/}
}
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Abdelkarim Boua. Some Results for Endomorphisms in Prime Rings. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 6, p. 943 . http://geodesic.mathdoc.fr/item/KJM_2021_45_6_a7/