DESCRIPTION OF A NOTATION FOR THE LOGIC OF RH.ATIYl 



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If we take 



we have 



If we take 



we have 



i 



3 



k 



I 



m 



i 



) 



k 



Ui:u 3 + u 2 :u 4 , 



2.Ui:u 4 , 



i 



3 



k 



• 



% 



• 



3 



k 



j 



k 







k 













 

















Ui:Ui + u 2 :u 3 + u 3 :iu + u»:u« + u::u 8 . 



ill :us + u 2 :u 4 , 



2.Ui:u 4 , 



u 6 :u 8 + tt.ii 5 :U7 + 2fi.Ui:u y + u. t :u 4 -f C»Ui:ii6 



u 5 :u 8 , 



% 



3 



k 



I 



m 



• 



t 



3 



k 



I 



m. 



m 



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3 

 k 



k 

 

 







# 









 





























 





 



t.m 

 















These multiplication-tables have been copied from Profe-or Peirce's monograph on 



Linear Associative Algebras* I can assert, upon reasonable induct.ve evidence, that 



■ - - ' the 



all such algebras can be 



interpreted on the principles of the present notation in 



' Linear Assocl„r„e Al 9 *ra. *i»A»»*— »>,*>*** *" ii W- ^ 



