Sum Range of a Quaternion Series
In this paper, we obtain a result which implies, in particular, that for a quaternion z ∉ {−1, 1} with | z | = 1, the sum range of the series ∑ n z n n is a closed proper subfield of the division ring of quaternions ℍ isometrically isomorphic to the field of complex numbers ℂ.
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| Veröffentlicht in: | Journal of mathematical sciences (New York, N.Y.) N.Y.), 2016-07, Vol.216 (4), p.519-521 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we obtain a result which implies, in particular, that for a quaternion
z
∉ {−1, 1} with |
z
| = 1, the sum range of the series
∑
n
z
n
n
is a closed
proper
subfield of the division ring of quaternions ℍ isometrically isomorphic to the field of complex numbers ℂ. |
|---|---|
| ISSN: | 1072-3374 1573-8795 |
| DOI: | 10.1007/s10958-016-2908-9 |