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
Correction: Math. Comp. 31 (1977), 1031-1033.
Original Article: Math. Comp. 31 (1977), 1031-1033.
MathSciNet review: 0442043
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.
-  Leonard Eugene Dickson, Linear algebras in which division is always uniquely possible, Trans. Amer. Math. Soc. 7 (1906), no. 3, 370–390. MR 1500755, https://doi.org/10.1090/S0002-9947-1906-1500755-5
-  Irving Kaplansky, Three-dimensional division algebras. II, Houston J. Math. 1 (1975), no. 1, 63–79. MR 0432705
-  Giampaolo Menichetti, On a Kaplansky conjecture concerning three-dimensional division algebras over a finite field, J. Algebra 47 (1977), no. 2, 400–410. MR 0453823, https://doi.org/10.1016/0021-8693(77)90231-9
- L. E. DICKSON, "Linear algebras in which division is always uniquely possible," Trans. Amer. Math. Soc., v. 7, 1906, pp. 370-390. MR 1500755
- I. KAPLANSKY, "Three dimensional division algebras. II," Houston J. Math., v. I, No. 1, 1976. MR 0432705 (55:5689b)
- 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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Keywords: Three dimensional division algebras, the field of five elements
Article copyright: © Copyright 1977 American Mathematical Society