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On Division Algebras

1921
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Transactions of the American Mathematical Society
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The object of this paper is to develop some of the simpler properties of division algebras, that is to say, linear associative algebras in which division is possible by any element except zero. The determination of all such algebras in a given field is one of the most interesting problems in the theory of linear algebras. Early in the development of the subject, Frobenius showed that quaternions and its subalgebras form the only division algebras in the field of real numbers and, with the

doi:10.2307/1989011
fatcat:hpku6ograbck7g5x2m3pp6f2tu