Large Annihilators in Cayley–Dickson Algebras

@article{Biss2005LargeAI,
  title={Large Annihilators in Cayley–Dickson Algebras},
  author={Daniel K. Biss and Daniel Dugger and Daniel Isaksen},
  journal={Communications in Algebra},
  year={2005},
  volume={36},
  pages={632 - 664}
}
Cayley–Dickson algebras are nonassociative ℝ-algebras that generalize the well-known algebras ℝ, ℂ, ℍ, and 𝕆. We study zero-divisors in these algebras. In particular, we show that the annihilator of any element of the 2 n -dimensional Cayley–Dickson algebra has dimension at most 2 n − 4n + 4. Moreover, every multiple of 4 between 0 and this upper bound occurs as the dimension of some annihilator. Although a complete description of zero-divisors seems to be out of reach, we can describe… 
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Quadratic Forms Permitting Composition
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