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... Basic Algebra:

     The word sedenion is derived from sexdecim, meaning sixteen.  A sedenion is a hypercomplex number constituted from 16 basal elements.  A set of sedenions form an algebra, S.  If S, T, V represent three sedenions the algebra is

  • Non commutative :   ST is not necessarily equal to TS
  • Non associative    :   S(TV) is not necessarily equal to (ST)V
  • Non alternative     :   S(ST) is not necessarily equal to S2T
  • Power associative :   Sn Sm = Sn+m
Furthermore it is
  • Not a composition algebra :  n(ST) is not necessarily equal to n(S) n(T) , where the norm of S is defined as
       n(S) = S S* = S*S ,    S* is a conjugate of S
  • Not a division algebra   :  i.e. there are zero divisors ;
      There are sedenions S and T , neither of them zero, but  ST = 0 = TS.

Our Publication
                                                           Sedenion: Algebra and analysis
by K.Imaeda & Mari Imaeda
A 16-dimensional Cayley-Dickson algebra is presented. Its unique algebraic properties, its zero divisors, and the solutions to a general linear equation are found.  A theory of function is developed in terms of the regularity (monogenicity) conditions and some such functions are constructed.
4/1999 : Accepted for publication in Applied Mathematics and  Computation.
Publication date : 10/2000, Vol. 115/2-3, pp77-88