Existence of the \(N\)-th Root in Finite-Dimensional Power-Associative Algebras over Reals - Arutyunov, Andronick Aramovich; Zhukovskiy, Sergey Evgen’evich (Eurasian Mathematical Journal, 2017)
The paper is devoted to the solvability of equations in finite-dimensional power-associative algebras over \( R \). Necessary and sufficient conditions for the existence of the \(n\)-th root in a power-associative \(R\)-algebra are obtained. Sufficient solvability conditions for a specific class of polynomial equations in a power-associative \(R\)-algebra are derived.