Abstract
We introduce notions of quasi-spherical and multi-quasi-spherical polynomial quaternionic equations defined in terms of the shape of the set of the solutions of the equation. We establish that every quaternionic equation of the form
is quasi-spherical. We get some sufficient conditions under which a quadratic quaternionic polynomial can be represented as a product of linear quaternionic polynomials (and thus the corresponding equation is multi-quasi-spherical).
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Acknowledgements
The author is thankful to V. Szpakowski for useful discussions.
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Partially supported by State Foundation of Fundamental Researches of Ukraine (project no. 25.1/084).
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Mierzejewski, D. Quasi-Spherical and Multi-Quasi-Spherical Polynomial Quaternionic Equations: Introduction of the Notions and Some Examples. Adv. Appl. Clifford Algebras 21, 407–416 (2011). https://doi.org/10.1007/s00006-010-0250-8
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DOI: https://doi.org/10.1007/s00006-010-0250-8