Geodesic
Existence of the $n$-th root in finite-dimensional power-associative algebras over reals
Eurasian mathematical journal, Tome 8 (2017) no. 3, pp. 28-35 
A. A. Arutyunov; S. E. Zhukovskiy. Existence of the $n$-th root in finite-dimensional power-associative algebras over reals. Eurasian mathematical journal, Tome 8 (2017) no. 3, pp. 28-35. http://geodesic.mathdoc.fr/item/EMJ_2017_8_3_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the solvability of equations in finite-dimensional power-associative algebras over $\mathbb{R}$. Necessary and sufficient conditions for the existence of the $n$-th root in a power-associative $\mathbb{R}$-algebra are obtained. Sufficient solvability conditions for a specific class of polynomial equations in a power-associative $\mathbb{R}$-algebra are derived.

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