ON AN ALGEBRA IN THREE UNITS 



133 



II. As stated at the end of § i this algebra is reducible.' Making 

 the following transformations upon the units: 



ej+ie2 



(16) 



/ ^i ^^2 



C T Jv-^ D J I vV2^2 I " ^^^ 



(, X2 ~r J^i \ 

 where, ^3= I , 



the multiplication table takes the form: 



in which 



2 



/ = 2i(5C2— i;'(;i)+-(:x;2+i:Vi) . 



' For the definition of reducibility see Epsteen, Transactions oj American Mathematical Society, Vol. V, 

 pp. 106-9. 



