Abstract
We give complete description of possible shapes of the set of the solutions of any quaternionic equation of the form ax + xb = c. Moreover we study the set of the solutions of a quaternionic equation of the form ax 2 + x 2 b = c by the method of sections by hyperplanes perpendicular to the real axis; for every case where such section is an unbounded linear manifold a necessary and sufficient condition is found.
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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. Linear Manifolds in Sets of Solutions of Quaternionic Polynomial Equations of Several Types. Adv. Appl. Clifford Algebras 21, 417–428 (2011). https://doi.org/10.1007/s00006-010-0252-6
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DOI: https://doi.org/10.1007/s00006-010-0252-6