ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

Discussiones Mathematicae - General Algebra and Applications

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Discussiones Mathematicae - General Algebra and Applications


Discussiones Mathematicae General Algebra and Applications 24(2) (2004) 251-265


Raoul E. Cawagas

SciTech R and D Center, OVPRD,
Polytechnic University of the Philippines, Manila



The algebras C (complex numbers), H (quaternions), and O (octonions) are real division algebras obtained from the real numbers R by a doubling procedure called the Cayley-Dickson Process. By doubling R (dim 1), we obtain C (dim 2), then C produces H (dim 4), and H yields O (dim 8). The next doubling process applied to O then yields an algebra S (dim 16) called the sedenions. This study deals with the subalgebra structure of the sedenion algebra S and its zero divisors. In particular, it shows that S has subalgebras isomorphic to R, C, H, O, and a newly identified algebra [O~] called the quasi-octonions that contains the zero-divisors of S.

Keywords: sedenions, subalgebras, zero divisors, octonions, quasi-octonions, quaternions, Cayley-Dickson process, Fenyves identities.

2000 Mathematics Subject Classification: 20N05, 17A45.


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Received 19 May 2004
Revised 25 July 2004
Revised 30 December 2004