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. 
@article{EMJ_2017_8_3_a3,
     author = {A. A. Arutyunov and S. E. Zhukovskiy},
     title = {Existence of the $n$-th root in finite-dimensional power-associative algebras over reals},
     journal = {Eurasian mathematical journal},
     pages = {28--35},
     publisher = {mathdoc},
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     number = {3},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2017_8_3_a3/}
}
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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/