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On the Subalgebras of Finite DivisionAlgebras

Published online by Cambridge University Press:  20 November 2018

Joseph L. Zemmer Jr.
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In 1893 it was shown by Moore that the only commutative, associative division algebras with a finite number of elements are the well-known Galois fields [10, p. 220]. Twelve years later it was shown by Wedderburn that every associative division algebra with a finite number of elements is commutative [11], and hence a Galois field. It is conceivable that these results, particularly the theorem of Moore, motivated some of the work done by Dickson and published in two papers in 1906 [4;5]. The work referred to is an attempt to determine all commutative, non-associative1 division algebras with a finite number of elements.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 4 , 1952 , pp. 491 - 503
Copyright
Copyright © Canadian Mathematical Society 1952

References

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