From 61b60c6880e9fe83402da76a9c0d5d39c09cc679 Mon Sep 17 00:00:00 2001 From: flavis Date: Mon, 16 Nov 2020 17:00:41 +0100 Subject: [PATCH] fix typo --- ws2020/algebra/uebungen/algebra2.pdf | Bin 141169 -> 141241 bytes ws2020/algebra/uebungen/algebra2.tex | 5 +++-- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/ws2020/algebra/uebungen/algebra2.pdf b/ws2020/algebra/uebungen/algebra2.pdf index 95bf8d53ff37bed16daa03f4a51391138697fba6..ee406ed39f5d10b18e1387fc726a0240734feba2 100644 GIT binary patch delta 5163 zcmV+`6x8eS&Iq~B2(S$z12i)=lVK4kf9*WkawEr)@ADOS*at8~lc^ zlTuEvgpk+!_3ie0HQ(+0J2~YSGiH>N(?9RuUMMx4Z{u(NcfVTQSIg>xO*b%PdKn-8 z;cm0s?w0d)y!}hH*;VU{pWpoH#W!zW{PP6^4C#c`7*R)rFA2Q*DQ8}3bnWT=-zs3-uL@^Dte+nc1-p9ZZ zDiq+sSc1;`2xy{V?pZeI3uLNr)tM=W!WiMIe*eYAjB`F^2~N(z8FP*pXG`KOYJpqK z@0W>*%gv@*?0;Kc128+SR`Kb!S|+Kx5B%9~NxXfzuR&Dn4uDmBB6A6-8WFIi2t<@+ zhO!WpXxA+MigJmp-?PHhe`7eZa!Ukd^?+&vni&_Cu-z_y@wnU}w4ZUHt^lPzLEuyz zWDW@&dsc}{XbNmWLJ*@JEQ}KFPEjC>ug9PYB%VQm#5onHJChz!)wtArrf0JXlE`wV zE2=0mnE)2a5xXE=*DwGuhRFq^ideznLW37`CkTf7WP%}%5e#t-f58w3ZMZmUCUKZo z-n!5e$zqEsJXz?d$f#3D`IuIBCUCZlVj|lxI9%_KJ;-=5a7ro+?+Vd&3&de=1Kgvh`;Rc z8_a?LT|R-|wRzy5f5bfKBg{irX-`x+_8Hp^&+Gx*IR|}slH({+9&Q;?x{TgmwTVv1 zT#H;F<*%Zbut+3f30ES%UHi9?v&IDWApjjrE0_SfYW|3IRO&St=J z9Y=7N!{8u2O%dXCpTU|?TMF4w>X!}q3A2!pznc*s-ALNc7-OXXN%BJL7p{_RxUITn z5pN3n6lKN`f5vtB;~NA|Nt|t*&~dg6g(9_^WP^Tp0orUZfR2cu>+M*M12m6?r_T(J zVbQB465@`>LX-&0dJu2N*!30aOO=DQ#w3jDyauf0wEE!7(oMD6U##Ps+iE@E_r=s& z0z%fQ+LiL*EQe@PvxK$8>I_D>$t)WLk&yryW*S)mf0rQkO~s_+;C1fcbzYGyluPE> zj6`dVx(%{%Qvr&@`EjN~9WoWAVhq^|du%+9*@^-HiDY`UtRjhu8ZX>;DyuNGsjPmqwTW+%aRI5)ib&QmM&EB@0JYe^-TBG5oW@`BUTvB8YRf$5B-{+R25{y?adkv( zSs!u@e^E>`3c-x8<`LDfd=r)rcfobm2&GF;E;Fr`X(8FNua~REetjEX%omG}Ze1qo zflO0gQ!fP|yG^yLjrh&O3KVdWYVO}9mkD!RFW2+k@?qUr`~6J}Xqa{(gDc#=kJguM zke!oAP$GqFRU%JNSPU<+96}|IKN%H{POjkEV3QBc z9)EDe>|$U(?XbnZADqsQN2lZH@(ObgTx)G1Ztr1?VV%9US26yR)0gYt=69=j9dy%Q ze3$gj%a<3`r5Dvk%>0OVL4+UT&Fc&6EkS|;<|Aw)`s>zkNUlI1Htp?zniP2aShW=?m-w0WX|oXK<1_3Q-y}QoI{u)0SOVdy~7W3DQ&FaC9uQEhPK>^%+!2^ zc?M0Sa>ZIZ9!7^LX?HPY)Wsm3JcdKM!y)m!9O6&lkclKOIOMGoX7-rM^QOy4fB2RO zGBE*EXNVD!6U$|H`}YVw*d8AaY#|%s+OTf#6IK+__X9{Oz@ZJVhlItPfF$eq7bJGm zgtfsND)c0x{_Q$0=WqLaFn&QKAYe(27MX2?pzQ(C1h_O!jHEiAE_d>>=Yz8qVA5d) zL^loDnz*lDp}TBSRt!N{gOm;Tf12DtmifEy-RY^09V&J*k)dx;*%qKFvVob!t$2kI z>x${G#rNSH%0G%cj)cyjx~b>O*P=9zpnRJ8Oal_Tq|q<;H@EX^A9YSWQdUf538V#9 zOsh4~%H&%E^V%!rKPl`9WN*}VDg@o&+uF{CMX@~~U;y`(1i^cI5;Pkqe?qyi%!3Nc zX~0(LQw(S8a&;uRNMJxiL1=3ODf+EhOfj(1Y64jh@t_YhXK}EkfdH{ND>P*l>(@R% z6A%jeeG)!wTsTM~^N2~Ihf5>AGT4y&ub5r8Igx5g7s+kWl<)%vgSke2pPsS?Hq4x0 zP1RMFn+cv1Eyh@d351`Ef5wl$N2CYj3)YzD<7W|}BXasziM)VfrjA^YMqODvJ4hf40)sL10rFMWnB@m6CK{;wjxo#XV4|2>r zsPmWy1^jhR3`Z+KMjonlQarz^s;8>z@s;Q^sOk(-RtP>>24#8i`cEv$lJr{Ftg01RRi!3y4Q<)86P}xvAdPUA_C%)f=mD@Z?o> zMTJ~1eH>W^2#`jA2#1`@f&#jhEZ3tEfhAmzZ(L{P-r*g>Y|w!cQ<$;g%W`|L0oDim z>B$DsC#!uFRq9hGe}~8v>ay;-#a)u)Y_!E_oDTAFbVvo0b=9__Z+F#d)wK7n@#SkJ z4z0f|rrynWUBTf_5vz4ya(+Q1$98q1XiVYg&Wcsd^l4WG+aQH7sg3goItvP3HgfaU z2k^c=yG(7*|1;me+btK>e06|w4%D?##vf5mN`AhWX}rwee@Pm2u`4Y7c9QR{f{aP0 zX!7^fuhnwf{b3nmn2<-NIbN=BePN8!sXrnhDVtUw>IXHAiX|EvdZ){nr{gzm>k>J( z??U|vh9{EwNjtBam{vpl{&!#YENH$tqQmO6@K0D5cE;e}kaBRa0IiTbQ9B9@FC$+U z^YuD$_yfTzf6^An%Q`NyvybVl`S;>5uX%&uLW#7Q#LpPD4Ovtf3(~d_*-#sy5BIGf za)dzaSuM>>0=n9D`Uhh3)M~Y>maA%Wv#FM089Z!X?c!zZ7oo8*a`UjcuU2W$V!qv` ztLhf3PpPm?e0HUBA}AI7qxf!fn=U0x+xk>VRRcrqe~59@VodZ~^ZFwynwjvENXnOc zh-pmNSzOdxi}&$Wvd4VD9$O3ZH5lEYC}-io(I|fo(%9&2H#jxD;MA5SMBQ44ukoy{ z#V2X>9j?*Z<({7I+RK;i(*TM>xnL6|mxfaiFd4 zVS>erV6mx`hZLh&_$SG{Vz1YsfN>^)T7s2r7_8WQLd71WqAf?;yc}ZN>4ITS2b>XmFC=kHpQJtm>=0w@5M6d4`-6l@%nQmPvA&{QjWxbuuGAZq zhD85827#6Z&0g)PK^YI>eNR+Q;h_T`5Q7;}ZhwCH8eALz5E7(0X}1aGHfA-v#aIomDE>b3a9Q_&8bg_zH3Q%sx)jo_bNYoD7tv+v=|B3=Ak%l$ zoYIENl?}Gl{|~m+UqsuwZaT^O7PX)h#DrR(As;}_E)a)3mi+(8J?4nw)@sgcuTj>9RIYSE28oKFYLcgc z_;8@#jY6_5-A8bxhH%%+<1q|dUFmFs(DiwtyoIn4%zDEt>@=pYS8h zX|C@StC4C&RD}u>{6l+mImjN*D+U{?_H@WQP|XN?o=zNXklH7B zAbYTmWb}Cg6e;PZ8g%|?LV*`6BCw53oj@+~iGcLGo zk{$pWIz-eX7Ccx6IHFQ=DDf`KOs02h!7XJ5Z7s55Q3qhP=2UQXEICkXeRxj>gj= zJz^tz#GhS{PHb%*f6=3GW~lwnX5Xi9|5XOCQNSGF6>sbO$cdSrWO8c2Myg5til09C z#n(ieOsvWvCPH%2*$=5gGfY4-$&a58fxtpK`gDvfC`|oXf_ShELR=SuOp}$>JL~Y< zt4^GQa0${F;p$4S#wG8Re8Rkup z#yD1^H_99MgeifflUR~L=8`OuNjzi@nMLN41!NwX zO%|%-_FKJdGK4rPVfl78f&`GEe=2bUb{0s6sib$Jmz-eo8!UMPa+|@@T#)A`A3=V< zJsU}a$tV&+LP;12CvFl!B2|{v;qCHtu%Zfh8$f{{tbAbgqR416hKwcAB!-MrS@jhk zuf7h}dok-TpD2OdxS2US;cBf81{S1-7%w zj%=_q3lvv^UDd$X1a{|;KcM6r*z*FEmVvzqU|%G83HCn+WzRr4msk-E4jurNHQ*43 zKFp#=-hrcCpsENQW2eVk!HIHkvJadZ0H-->bu2i;i?fBG#s_M9L0u|1*9Pi2N5dD; zD4>bUY38$*G;rPpF64oWe;H&Dw0;6@e}VroxbzfU?gs7m!4(eJ!Tzp31f3n=8b|2j zI=f$ip3mS$1h^RkZl#c);7&5QTMT+DZ0(68iA+?vciYY;sl4`CN>=&TXDLNBKFHE! 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Es ist $\text{ggT}(X,Y) = 1$, da $X, Y$ prim aber $1 \not\in (X) + (Y)$, also $(X) + (Y) \neq (1)$. - \item $K = Q(\Z / 2 \Z[X])$ ist Körper mit Charakteristik $2$, denn + \item $K = Q(\Z / 2 \Z[X])$ ist Körper mit Charakteristik $2$, denn $\frac{\overline{1}}{\overline{1}} + = 1 \in Q( \Z / 2 \Z[X])$ und damit \[ - Q(\Z / 2 \Z[X]) \ni 1 = \frac{\overline{1}}{\overline{1}} + \frac{\overline{1}}{\overline{1}} + 1 + 1 = \frac{\overline{1}}{\overline{1}} + \frac{\overline{1}}{\overline{1}} = \frac{\overline{1} + \overline{1}}{\overline{1}} = \frac{\overline{0}}{\overline{1}} = 0 \in Q(\Z / 2 \Z[X]) ,\] aber $Q(\Z / 2 \Z[X])$ unendlich, da $\Z / 2 \Z[X]$ Polynomring und hat damit unendlich viele