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.

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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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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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