Corrections to Dickson's table of three dimensional division algebras over
Author:
F. W. Long
Journal:
Math. Comp. 31 (1977), 1031-1033
MSC:
Primary 17A30
DOI:
https://doi.org/10.1090/S0025-5718-1977-0442043-3
Correction:
Math. Comp. 31 (1977), 1031-1033.
Original Article:
Math. Comp. 31 (1977), 1031-1033.
MathSciNet review:
0442043
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Abstract | References | Similar Articles | Additional Information
Abstract: In 1906 Dickson published a list of noncommutative division algebras of dimension three over the field of finite elements. Recently, Kaplansky has found a mistake in this list; and I used a computer to check all the entries in the list. I then found an algebra missing from the list and used the computer again to make a complete search for all such algebras.
- [1] L. E. DICKSON, "Linear algebras in which division is always uniquely possible," Trans. Amer. Math. Soc., v. 7, 1906, pp. 370-390. MR 1500755
- [2] I. KAPLANSKY, "Three dimensional division algebras. II," Houston J. Math., v. I, No. 1, 1976. MR 0432705 (55:5689b)
- [3] G. MENICHETTI, On a Kaplansky Conjecture Concerning Three-Dimensional Division Algebras over a Finite Field, Mathematics Institute, University of Florence, Italy. (Preprint.) MR 0453823 (56:12076)
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1977-0442043-3
Keywords:
Three dimensional division algebras,
the field of five elements
Article copyright:
© Copyright 1977
American Mathematical Society