Geodesic
Some Results for Endomorphisms in Prime Rings
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 6, p. 943 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 
@article{KJM_2021_45_6_a7,
     author = {Abdelkarim Boua},
     title = {Some {Results} for {Endomorphisms} in {Prime} {Rings}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {943 },
     year = {2021},
     volume = {45},
     number = {6},
     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/