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The all-associativity of octonions and its applications


Using an elementary method, we give a new proof of the all-associativity of octonions. As some applications, the known Taylor theorem is improved, and a new definition and new properties of octonionic determinant are also obtained.

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Corresponding author

Correspondence to Xingmin Li.

Additional information

Supported in part by the Doctoral Station Grant of Chinese Education Committee (20050574002), P. R. China.

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Liao, J., Wang, J. & Li, X. The all-associativity of octonions and its applications. Anal. Theory Appl. 26, 326–338 (2010).

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Key words

  • octonions
  • associativity
  • permutation
  • determinant

AMS (2010) subject classification

  • 42B35
  • 30G35
  • 17A35