Corrections to Dickson’s table of three dimensional division algebras over $F_{5}$
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Correction: Math. Comp. 31 (1977), 1031-1033.
Original Article: Math. Comp. 31 (1977), 1031-1033.
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.References
- Leonard Eugene Dickson, Linear algebras in which division is always uniquely possible, Trans. Amer. Math. Soc. 7 (1906), no. 3, 370–390. MR 1500755, DOI 10.1090/S0002-9947-1906-1500755-5
- Irving Kaplansky, Three-dimensional division algebras, J. Algebra 40 (1976), no. 2, 384–391. MR 432704, DOI 10.1016/0021-8693(76)90202-7
- Giampaolo Menichetti, On a Kaplansky conjecture concerning three-dimensional division algebras over a finite field, J. Algebra 47 (1977), no. 2, 400–410. MR 453823, DOI 10.1016/0021-8693(77)90231-9
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp. 31 (1977), 1031-1033
- MSC: Primary 17A30
- DOI: https://doi.org/10.1090/S0025-5718-1977-0442043-3
- MathSciNet review: 0442043