Irreduzible komplexe Zahlensysteme. 309 



Y) Untersystem 



«i 



















e x 























a) VI 83 











ß i 







VI 84 











e i 















6 2 



















e 2 











C l e 2 



e 3 















e x e 2 



e z 







e l 



e 2 



e± \ 



4= 



i 







e l 







«4^1=*=! 







\e 2 



e x + e 2 \e x +\e 2 



^ 











\ e 2 



e x \e 2 + e 



1 *5 



e i e 2 



H 



e i H 



e e 







e i e 2 



e z 



e ± % 



^6 



rec. Ai zz 



1 )' 



_ X 2 \l _ _ X 3 



-hX t -f-l 





rec. Ai 



1 



y _-X 2 + X 1 + l 



VI 85 







e x 







b) 



VI 86 











e i 











e 2 





















e 2 







e 1 



*2 H 













e x 



+ £ 2 e 2 



h 







e x 



o ^ x t 4= i 









e x 



+ e 2 



e x 



e 4 \, X 2 z 



A 



1^2 e i 



^2^2 ^5 









A 



X 6 2 X 



2 e i K e i+K 



6 2 e b 



e i C 2 



e 3 e± 











C l e 2 



«3 



e ± H 



e ß 



rec. A'i zz — 



,U = : 



— X 2 -t- X t H- 1 







Aj zz A2, Ao 

 rec. Ai zz — , X 2 



1 



X3 = X 4 , X 4 



1/ — X s 

 , A 3 — , 



= x 3 



X' — — i- 



XjX 2 



8) Untersystem e x 

 f 2 



a) vi 87 00000 <% &; VI 8 



e 2 



0^ X 2 e 2 e % 0(?j + ^ 2 e 2 e 3 X 3 ,X 4 zjrl 



t? 2 +X 1 e 1 e 2 +\e x e 4 e 2 +X 2 ß t ^ ß 4 X 1 4r x - 



ß 1 + X 2 g 2 \e x \e x + X 5 ß 2 e 5 



e x e 2 e s e i e h e 6 



für \ = : X 2 = — X 3 , X 3 = -X 2 , Xi z= B \, X' 2 = s X 2 , X' 3 = X 3 , X 4 = X 4 , X 5 = e X 5 , X' 6 = s^ Xg 



X4 = X 5 — 2 X 3 , X 5 =z X 4 — 2 X 2 Xi zz X 2 , X2 zz Xj, X 3 zz X 4 , A4 zz X 3 , X 5 zz Xe, X 6 zz X 5 



immer: rec. Xi = X 15 X 2 zz — X 2 , X 3 zz: — X 3 , rec . Xi zz ^ m , X 2 zz *3 , X 3 z : — , Xi zz ] 



^,X 5 =zX 5 -2X 3 . 













e x 













c 2 







e x + \e 2 





C 2 C 3 







e 2 +X g 



C X 



C l C i 







X 3 ^ 2 \±e x 



V 



L + V» H 



e l 



e 2 e 3 e i 





e h e 6 



rec. 



Xi 



— 



^3 



•-u x 4 - 



- 1 /* 



x 2 = 



>^ 5 



X 4 zzX ( -2X -X 1 ,X:= ) =zX-— 2X 9 . X 3 / S X 4 A X 4 : /s X 3 % X 3 X 4 



X fl 



J Xq 



s) Untersystem: 



X//a X 3 V 3 X 4 '/ 3 X 3 V 3 



e 2 



a) VI 89 e x 



e 2 



e x e 2 e 2 e 3 



e 2 e x + \e 2 e i X 3 z|z 1 



X 1 e j A, ^ + A 2 e 2 ~k±e x + X 5 e 2 e 5 



e x e 2 e 3 e± e h e e 



X'i zz — Xj, X 2 zz X 2 , X 3 zz — X 3 , X4 zz X 4 , Xg zz — X & 



recXj = -=^-, X 2 = =-l±l, X 3 zc -I, X 4 = ~^+^~\ X 5 zz ^ +2 ^^ 



*V /a " »V /S X 3 X 3 fX 3 V ' : 



Denkschr. d. mathem.-naturw. Kl. Bd. LXXXIV. 



42 



