Corrections to Dickson’s table of three dimensional division algebras over 𝐹₅

Long, F. W.

doi:10.1090/S0025-5718-1977-0442043-3

Corrections to Dickson's table of three dimensional division algebras over $F\sb{5}$

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
Full-text PDF

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)