Large annihilators in Cayley-Dickson algebras

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dc.creatorBiss, Daniel K.
dc.creatorDugger, Daniel
dc.creatorIsaksen, Daniel C.
dc.date2005-11-28
dc.date.accessioned2026-07-07T06:51:50Z
dc.date.available2026-07-07T06:51:50Z
dc.descriptionCayley-Dickson algebras are an infinite sequence of non-associative algebras starting with the reals, complexes, quaternions, and octonions. We study the zero-divisors in the higher Cayley-Dickson algebras. In particular, we show that the annihilator of any element in the 2^n-dimensional Cayley-Dickson algebra has dimension at most 2^n-4n+4. Moroever, every multiple of four between 0 and this upper bound actually occurs as the dimension of some annihilator (a theorem of Moreno says that only multiples of four can occur). We completely describe all the zero-divisors whose annihilator has dimension 2^n-4n+4.
dc.identifierhttps://arxiv.org/abs/math/0511691
dc.identifierhttp://arxiv.org/abs/math/0511691
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105120
dc.subjectRings and Algebras
dc.subjectAlgebraic Topology
dc.titleLarge annihilators in Cayley-Dickson algebras
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