Existence of the n-th root in finite-dimensional power-associative algebras over reals

The paper is devoted to the solvability of equations in finite-dimensional powerassociative 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.

Authors
Arutyunov A.A. 1, 2 , Zhukovskiy S.E. 3
Journal
Eurasian Mathematical Journal
Publisher
Eurasian Mathematical Journal
Number of issue
3
Language
English
Pages
28-35
Status
Published
Link
External link
Volume
8
Year
2017
Organizations
  • 1 Department of Higher Mathematics, Moscow Institute of Physics and Technology, Inststitutskii per., 9, Dolgoprudny, Moscow region, 141700, Russian Federation
  • 2 S.M. Nikol'skii Mathematical Institute, Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
  • 3 S.M. Nikol'skii Mathematical Institute, Department of Nonlinear Analysis, Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
Keywords
Cayley-Dickson construction; Power-associative algebra; Real algebra
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/5951/
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