From ad9faf151bd7a77dac6d5663b27615b9d3544418 Mon Sep 17 00:00:00 2001 From: Gabriel Antonio Videtta Date: Thu, 7 Dec 2023 16:49:42 +0100 Subject: [PATCH] feat(algebra1): esempio sulla corrispondenza di Galois --- .../main.pdf | Bin 227646 -> 229014 bytes .../main.tex | 30 +++++++++++++++--- 2 files changed, 25 insertions(+), 5 deletions(-) diff --git a/Secondo anno/Algebra 1/3. Teoria delle estensioni di campo e di Galois/4. Il teorema dell'elemento primitivo e di corrispondenza di Galois/main.pdf b/Secondo anno/Algebra 1/3. Teoria delle estensioni di campo e di Galois/4. Il teorema dell'elemento primitivo e di corrispondenza di Galois/main.pdf index 64fa4d5694de03bc61fb75e50e326dd13d354ff0..c0e6bc9320f77bdcb4eaff3a37c71f710fa2887f 100644 GIT binary patch delta 12293 zcmajkML=A^mH<%b#tH5OY200#;O_1c+}#o&K;sacAdS1bOM<(*1_|yST*B~YW;cu3 zohw!MZC)*^I{cH z;ew{lZ!@;hoS4{_*_OmS@#S0jlURLOabd#YI^hnD6n;g;iP3`6?7&VCYv<2`tB0YM zuU&6kUr`4mG$PqHI*keCs69~&NH_+WH&_Y&XhFWMHQqPvmj8Cf2tV_iP-^;3uAKq# z`?X$q8C#ul_KM;BcKs}Z%F{pCN;~OBI8OCsA21?g5u|#AJshV*c;vdo+yZ<1k4BJo z?~=nYBA!<0P6?}lx;GN8-T`8Jzq-!2X*@{er$cGro?j^}!}FDNAqPs|C_ya+SjQZ~ za1Nl9s*v5BVmqV7EUO^D&|3(Zi)Dk9n_a=imJ&3XMAG-*^C%j~lg3k)swY$5H|MNtx%f;h6LFthwKo zf}cY%+oFj=xdINW%tznxJTR$`6}^s4nfX$RQ@kwNR}EH)*MOD@AKky+MKKZ5^lBjn z2gBsR+YvNR#K%tMs?5=LTnUg~zGwkaoEhFaeq`WpXI`~xK@^`SdrNs$h{pr z=B1b)8s0kOSkZEie`B+b(8<0TCEXnGJ9RjPQ$LR%$-Bk=ekz+Tn`n#$n=Yv|9ci1~ zf2~7MWC(SP7shv?va2LAWp@g~qx*dhRjxES4Sm-zS(I^F0OmOx<%|w+YF z`ZcR(T2((UFo`y-8EM>57=nsd7VyDOl>=tg;j2n%>sFeX;HG}SdX{GkuUP!BR|!%$ zl9szXHGy8YhC}Y$24nNqG3UlDF%Ajv-|peR-QmRgV_4AdaL;GVoLDHi&c~ZHWJ?_9 zYMqUimE&oA1O+N@zGX-ZrrE$p5vp{=fD&4MdBSmf41{RU4|FcSGk6r88VntUJ@|N~ zF06PsI{5xs%KlL{WJH{ayFSBNA|O>%;M7hqb|Bc;G8&)Cs3 zg-J_1bw5a@ak73wirgn~rJAh&<=M~q1+0$mKzy{8O{a6cls^b*3^_i&D9vY@9$lv> zw~t&O#5T9Ao~`ivCE`(S+T@HLPP+%3sfySYjocb9sd$#i5UP(>KEN8W`BAV}Vi+6X zF0pXphdvZ7DVc+_v$FJ&dR}X4;vA;hY~94Jj|F~5db@ApI^=S4I9}-6Lb^gqS(aIgxP zNh<^!u-kPI26Qk;+sDWFuDi%J{N1wq{_~8zVPA5GrzW(BgVeM`STV-7FIDY4T1jb! z8Nq}Db@}|>QDa_;oAp~8Bl;|2VhKD75(1y8k)k-}@wtjKaNX}7XvDll7D7%LWArj6A?%s$+VOCAo}u2BrkY1{Wb=p8tNzC)KGCdS?S%q7 za{g97NUrJO7j{S*PF>JSMxK4kbY)${sCUR^@(qd2%CfBMk(XTR1-zbBy$HqNkZgDV z`Dz>9$fWC1K@d8nafPsHw7;A_y^NX7=0=2-!LTXQ^Tj*ovd$*;w68e+CUs>%JXgQ2 zX57qwatIRk3=`NS4Hq!QKc=jX7Kq5qtY;42Thn4A%<`4*lF$3{@mw_FdYYR?$7lnB zvT7RyH}+1Ukl~ei!ZvH+`LPTMs7{)vy+pTz5&ITUEzwjfof5zHT6X8IO|NVlPB0OI zm}fF44%3y{yBPs`eawI3O2g(3UT+eH5qwoMaNE(AFgh>$8@`{So(npxP5|$^wJ$c{ z1J-%hAuG5zuArb>qkM(v9tpzq5`N&&Ly6mH)r}~ME(oMmA-VQ1TaBR7NO$}kj7Cez zu>V)^BHdA2rJF>AOMmghgo)_g)hs4ZO^Zl5$(8Sbf(*J3$9OC@jgrVhFH@ERhjFkB zpD?--3w-8{u7xb;;YckUCDE^W!*nfW<-L7_EIFlPw2=iAVM}H)i~Y_SJr56lCQ1g0Yb9(p3J2mSDh~fV$8SHS?;lM> z6O@atgVNpal2KRtu16<7x$it98XZM11&uFVEdhT|##Ky34KNIF7KUkR6ag@N^H}TS zR(<##M#yyog;L?#B-9hVsjz04Obl8o3U-M9FppWysqL9YxNPC z5OGwmxRW5OpLY%Tn((7Ak*GQ?;HMA;0d^d_ry#^uw=l5Dzm%vy5nz#I_YbgYm)!1f z_zmNey_q3Q=CS{f^ zu-VKdN_!|d)`MNXkY=bVie73;+@PB3g2sRw_#NkaAn5lB(b$=W9$N_nv$3C<>&(Tn zo_}G@V$C;mzqo(TN+@pBvz0SYy2WZm(mhe)$5TRj#^En8+!2^|b&FV8`zz-FC7gPm z;K|vdr8c5**syNc@^{XD`CeAnDx;Jsh0MATIVc`55uLncvvdZ#-NpMp8x}`{4?=%*>P+@$xIygK@KvRO@`yay- zExD5k+bU>R+M)u`6LjEy*&va8^>@yu;}5aqSkz#*(=lJUmD&!(=VN!Mvp-Qxw9A>* z(SSHl74dVvJV$t|H!I2SQI)HT)?F9Xdxi)_43)ibT+Bq0r|@FIhv)M}38VA6 zpWcRw67^CG9bzfvHVR&wFc>C{n8Ml=5^g^XF=F*$vtiif(xg6Z@c)K^XS!SyF=k>9 z@zDC^-L)>X^{)+rVS76?;1`Ls=;XpQPAlAKPe#^!5@Ob%AD;Mnd}X;DHptS7k83y2 zY}7olQ|;|zcl|2oe}s&*94w~U+J!y*Ajr`^MVhOLFoR-|e0%aJ!ghYRT@m`{8G`t4 zP!FDYXl#p3NT2KG5+Qm1D=-jvA`5>n*>pBiSHvM+<&Gjrr3LF0O++!0r*xk3sL!+ z)a(yHl@bu1LWfOy89$S?lDKt{1YBJ9u0)`-G#2c+cz_S_!6&zW2#1;QG4Y%1Un>Tl zCF2QcdQ0@e?W&U#Xl$uaeXB=8txAMkhwH1G(7-$#Krs^4UJtko>knIXBhvPq-1qm#P!1=V*^eVO%u9*01v+$Oz4|V;=b7)#mfIQTD#;<7LC4tK{_Rrqtet}WtU$nlU2IV)0Na%+VvTQ)c5o&7Lk8+R`0*FR)e z7!g|NtG)hG52N#0JF@f!$VFr)t*HlHSd6f@apc+O%poQFOaLTM~_L5XJ&#^Tl|VZ;6L?p?jD&+M`VL@y=Z!q_ua1OUGn z2vRTU5khGj5L%XW!&awVo-yV%bUh*K9V%4!O6C{a_Aa*%GeJxX@{ex#US%(L(a23G zs>n9-Rc@tq`tWYw?C4tcpeuUDqf`1@<&hrO3m>GsqW)mFh8B>tnwZ{|fYWo8-90`e zyK}35OUXmwgezCvZw_dP-Fo6d8jvl*Uk}yaEReQiR?1Ut1V;JO>vA8!S#Cixyq@G~ zEMf_7_~T0oaL)9K>pSHGsTyt;HSJ9g(Qs+m*u)r2TdceX9d^BO znTuAi4WUvX0Etq~RRE`-<&P+&h1m}7Jo@s>sNc6Yfn?R(h4|}5l19O?K+fa{Rpi54 z>{cV1{)BjG$(Rt_wmB~AQ8fGkO@duba@6upMRlI}6#V=RrTpz>vi_o$#C&=NeoYL#3B+xwD8YCE=dYGk?>Y3X++0>u4{Vh~H;kXvUT2ADYRh8@v ztNVcwZks5K{$|7wP!j1jaK^t#PTj#fHYdH^$Iri&UB77wiBmW5f_Pns8)2h zY_NX5uUrQ=D%l2Qg_B(!Ji-4wOA!n=ah^&BpR9{-F7kbEZ8#txg5gpj{Do}*=>Q*d zolLstuy~Y;i9r%laUIez>m#1X_|*&w`%~7e3Jr*v$rmhbxK17akRR2(4LHQt*kTf= z$$g_k^wt(byUlQg50*?A$-r%t;4ul#_E@{Q9x2=T!F%vfT8I{OvAa=5{^I!3bwm{_ zf-y$sTR;v?q=39yo-b<}{aLX_=u%m(Gn>{xF_1a#*}$5j+cy!P+ziXRCp;y^^QTK< z=VW394;;(>EoH&(ssq@9qsD!|IZNSn?j>);<34`;!Rhya>Qs1f6EbD`$n*e)fg2S@ z+)U`7f-RIv$VO4-vHBs0dl3~PFve*O3uA_|8PyA7*MgV`RlC;Wj4f??C_W6sxt}Nb z&U*DFLn(Sl8Hayx42<2SOsKSW6Tm()htO$C^bR;n^ZS1p{;r3lQW_R=LTME2oGpx> zH1Xt2G`&?qkEX)5*y*sn+IW%v%2?{-(?)NOku=r*r~P@Umwi*0@QnY^m`dfFDnfH! zgy56>5vEWSMe&=UeFtPP%lTi-$s{l)PKM2rqfeIck4vb@Cg#vo(B(fwjHsmy6iX)y zcMms9Q^)_v*~|`w2MjeO1L6R@#k$@ITnkFLgK);t)-M7{b%aOedP+~`p)v&&LF37ouo-Ueq zvk`ykt#vO?@s3YDgVN2(p0}{Gj_RJyUIvj<^ zAr=NP7g9-X^o2lYMZVo_wJ7S)O*f;vNk0eqaMY6Ouq*FE%t_~9=}4Q6KFn%FQlrmobC~ZS`#Nv-n0=GWdc3}qv`iP2r=6~Hdil^DN`o46c<*B~e}LYLT9 zi`PKx+)0*LxQ*9v7Bfzn825(PFj>360d=5-#cOEYUL=8juzpv;+bAvcwhR`xC6E?2 zS`^wc@lFbB*m-fN@-Zx43raa`B^9(15kSx~J^>p@0@Y-Cr};6g0x6V66@b^$hX_cd zfNh9)Au zbA1W$L=UyW2jVuJ080>{#_vCFOA#Wl7aclJ^-dpr;65VsfZ?6)WI!q)^n&@FWfVYW z0Q8>iorhGwI{=i43y1@KXJbnd9Z(zqHRgRUJuv`p0njAyd+D7GEln&yF#vQ(5QqmA z;R4pTbg%;*0nir_pgvUfoh?^f|B2ZpfcVgLL7-$yD=%;r0JW6{;zBV+-`DF40G$9( z5&8G6R|SETKq#*AJKswbKWq?)N@~L zUc7k1^K~f3!FuL&KbTy0B`I;$rfak1^iy>hT-4E1r)g7qI=RpTVNoj?)cZY8=wc#~ z!B`uMrWIp`GBq-rQE1T@(iakhvL$JTx`ocdOvhgFJ48zrRJOG zDN+=1g*J!I19DBkK)#ru3kV1Wc+bLINb37Zm!LCPD>RU$AUQP9nXQdGnp zlz2(sHVWa$!Rb=V9U#YN@Ibrhm(0-fY=OSX?CGyH*<^~ZdZ;paYk8n+*G_qiWT<5{? znTTjE8(ZSj-)nPdjDX*F(mw;PiJyN*z}AZU1g`}YwM$5a2n9Svl%v$cQM)dQ&ec%` zPGKj@e>5W01rwTN^~M5udviZ*jKOYyq!b63sRh^(p3-lAhaha0s{J*Yvx!eDOu^q} zOt?GjA*Q}&L69*NFOss+rwWREIWd;E*{b(ib= zX8sv(FJs1=hdyV#xWewIK0fRg!rm`C@Gt#LZG~DyAn)%y03MPw zy2OhkOa-%v0E9An+BVo{Ri(=xVUL8^uFn5n+!4QwJo0&cmp&9YUMumV+1iTuN_+ zCZYf1iEJ-@ljRuYUJTDd*6)VZ6-`22#V+oQ6OuR^l> zmNg<43?T~A5UU{ny-B8S`-DrW6J!WxM;VCS%s_!9GmNrNV$;brtfPL+D9i=CY8>0& zSl_EMuXA{votNlF$2Mb>8}ohuBFMU+0U~rJ(OLNQ33{h71^8@JM|n>DBSeRZiP?pU zc2o=gB22)As%i)Ho)}zCvnVb3+bd0pEv2KkLuxUB&9Lw{ng3*>DRnl5<5t+??K>>y z=mW^DfadG~XJ=6SOe!K5{@hjX;0BXm`kC*#kY(~;+l<4-2(z@cr%a;Sfqnyvh4_-b zq!Ti?+F};Oiu1k3N?%#$B6C84;j^llOUFQpFQpOz#DMnXE*7%%6lkrFJzGMsRq;h2 zdbZYp=k|1u}NV|5_QWHM#7JVU3z)vdgBRss^J`$=&CgeKz_tMS53t3 z;Xr}})q1LZF$EhmYVvO9?xi4BaY}$UCY)F4Pk2#;JXg}<5qkRTtLzpyI-YAJh%eBE z8We&?JXpZ-oysde@X~8Z>(ko)6~YBflN@M}D5P@yWYl1>l15Q<+bj#itCCT72l z-8}BjBFk5k@Zow5bKL{}DUY)aA{p2y3;Q9;wzUeOU1@zR&n;yEpmNW7b6zgrCQcMr z>OMwQs7wh`R!os#)RoJW>J{X|*u+-g66kS=lDz*m?ZeoDKsX{6B5s!5PE&6xg>*Ymq)kg943FmlcbyLONQ`64|9;9=2~ z_(d}%T_uH3lCqrqTam86WU?a^;Va6~N)kVS zQ!zS0w6!w3G;TGsjx-f^kZp1IUmrWSc^ZaW_O;{VxIGw_0xKsTeT=9T`gyv3gj#E$ z{TzG>9#swuHc$|wr}vmd0kFWip=7Nc{JOXG&T8N5s04);rN{_|dSj5GMfZ7spzb%| zw!8FDqf4$uR@YE%h_4Pf7Ih04+D!+Ph+oLC+gj>V+y?jSVd0=|Kxobss&LhK5lEzV zGl|yygS8r6e%LQAMN*m~B&JU6DCgeyVMTvSW5;gbq}Y3P)MvQFtfELfqjPTZcslM% zyjX9aOZ`n^KI#6gj~Wj^r-WCS6|avj|7Wk``@GBL11w zFOZM+0oz?z-B|3WTx7P!s-yeATj@GQ_BM?}Vv(9edp{U`j{1G!b?fire!rP3aw8@a zHXPRi?QWj6+cvDLGY0+jp8Axzsxo5=NgMReLgKghad%UBtRUqA(Vkz;`hOb$6M2dc zj~bM}x+<1j7;&m(`MG2XhTcVTV_}$y#lYdQoa&$zVT8?3)A66x4LINo(R`QHfDPFB zAW>Fej-(rRZZK-I^vm_*UvPA2sqGxgT3uJH?MWy8?JY5S4W2KcD1oPnTSt8>Fg~8j z;9;}WKt^8Wz7}E=$`9n1k%2Fxa~B5=aUv^Fd7M}XV4-R%6(s~W)rm&Y`;#&Z?;weP z`rg1&icBrgo5&%5^CNpLHYI6EMzbyAb064)A`C^O1TQW7cV)aHRe3DX(ccKCoQ%8q z9-dJlsnCX*`Uv)#-AmrUPgJ0TvL(vW?eg&P!%Xx*MGqu=l_6-y+>yj&i6LT!OvrS4 z_(_zfgo_!b(xT&o1thQo_H4V%=f|#evQ4XyQ-&|s0~d@8!^h;q2%=+HOKr7;f2gC@ z!-aC^x}n~)7`Z*$>H0q7*gQwUc_x%RQqmGU{e2dWt+SVSge_qVHQ`iPvSCmz&=~jPX1_DzttunW*F;#`%Z}DUE(&sL9R583hqy zB^lL5xf80hE5t-j0%?*J(5K|G2$HmrN6n6T4-ylCGBffLF}vjxV3BT$27la?!t^z? zr&3o2%KHijrT2N_B!8vW5-e%N6%Yc01$W*r(F-ISBiuQAltk=R-F{+S< z9VUvk{odItXC;>g9pf!d=GdRmC@dNKnS5CIpVEtS(P+4T3{ZO^vq_jelR)A&Sq)E!^z8mYHc z@FU@G3Yi%H^%h(}PtxstvHvt7iz-R>?B(W%9;xj-jk1i<8`UwC`;oQ;jgS?CLMev% zEk5`a!%qI+@jlduboOP_?P$z@_)^^X(@pK@e-4ps``fj3M&NE%<*{Fk2&v^lG;X?O zr@d42HDH70N9W85PpUz_tx-o-2HYm>I91Gid$;GT$uL$Z} z;|3&uu1?8#SyIuTOg%k})lCP;xqD}3>t7;;iL_;B)X1?DE?ya8+ZG9H_1~BTVmyMi zx&`9u1v^VfMdEi)RUBUB8X9;YURq=A#fyKr^4p7K6tl?`O#t;^_RU`}-QrOb0x!5j z#WH^WTzpL{c5BX+((Y|+@L9(PrToIKg>*3~%B731w5}<*sn?RiBeEEAhqg{W%+#~= zA`@DH(%++Re4#jY*=>RQ+JEJ6vYhZtYl14)_>C{$uH@M$25GKG2m}= zeL2&~wRZlZwtjF@-RAYWsO!&|(kU2u@No7KE<@p<y4!7SE$?U_1JSErSRNn>tW|6U{N1WEdS=Up)c zuSWR4ZXIskx`UpM=oqT$^oc+M0>0fQXuma-ny|n#lvFFoGZOVzL<9Q!xDcag<%*~U zFMr-=dx5gfs&p#UObra9i42gAJ3{JC4a?=?(iPZvn%{`U%323fQqgebCQS57|5n*q zQ+~AK7EQ?OW%FfgYi9K|(fBSfoGs`6N|i~I#HSnINsYuWaa%COYC@*Q=g~{E6J`RO zW%M~#)M$Ti+f3WvdHUc>-o;49PGSL0am^5Wqv2f18gS;ofz2=cdoOg)hO>(>*|=hX zKH-~i{ui|v?F9hjbnk6cuE{V3s?#4~!Sgq&j=Gq6=m4f8GdhL9M7m-|D@w_ffY;CW z@6kX7Uq9_v7U*ue+~_c(nfjqM_H_0f_JFd}*2CuJqkTTj+9qB+A;W-#tw*cYc3L}M zeOA4oUJBadK$hXwzpaCop_+jGuYTGN{rY24?HCgujStNrYy;o+60g0z#XH~Zz0>EP zKkSG;qKWsktSsaUA}W!;>LnBG4a7Z4@xT`=sz;^AwvK5&i*Nw+2{OaC($xT!syfbMy111 zO_nkh@T*h}QbW<%so+bN^|^|1lQ%5sPsIXlyJ!wkh*|1*@ki6l3GLD#^LY8&p#_`z z6tsVVy8p0?Jq1898mD@m!+lwE!1s{5b1zl)s zmDDht8jZ7nDSa5`w^+?L);lFU} z)<7yRNSjhjzI)2@w8e`Cb;L@Jlm}ylv&+9t1FI~ya%lg*U2Ak|dO^22|GnqyL zdAl`x2?P#-Mvra z+so06!4J(iNT><<6}j3YdGtDPc;rq;yuTO$>_#{B^yOmYgpVyEQy39$i*j4#$g*1o z;(bMNQ~d`%CdEd3><^nvMN|xe<*1l`LdY8RH@cSRmxb^t#GJs>`&YcG^$^^@s(8kb ze^bcaVDbQN}9faPC(&?w+#K1>=Z8msCFC_d@2P*^*(WbsBB9$dTs&qi-XgwYe-_~VD3CB^ACJBK$jz7ENnJHL-Xa)ta=HD~`(50$(_=$ivUR_iB$s)8zf0aDAsVb3bpw(7>lWzww01XWa0NL1BQ z?{!{O?Am`4GN@UxtiQs}hl#VMn>_sxb(RJ5Y|MgdhHUf9&B9_QEG&OQmJiqKY_nM! z>t+nh-D676H&ZeWU>zLn1biSFkTIBXI z&&z!GhaTum8pRKBYK;-e;84~ZM?i1+_({wUv1N_%;P>!hm3P6xLk$f|wAg%7zq;?mmWxdBpH?9-v41qW*368j-~XIn;W3&-)H z>M#dN+VD>Si}TH#Uo=JrHtR4csAz19gq|AK?lEzLEtJexO-MSrI2fY@I}LkJ9fn6r z3P-{L_Jpt%erVxp(a(HTusrfdc%q{0?JfCPBfZD~EGD4p!ICcUYZhwVhw$F3%uU z>q|^EV!Q@iIy7DUVV@7aeB4;Eh!^RWb&u)t=M1uQ{vvF`;q=+HH%UIRmwUq(nON0d zSG%T0JMjuv>YvYNCG>mctIWFP!vP2^Gg(&}6iXF=1K?qY3K;`~>3O;NdH9*wIq2Bg z=@?Mhl$f95FSn=6gCZ8A4?Di z4<`zn4#(&Lhsl2bPc&;{bCCgZ}>(wD&>(d&$ks!Sz4ydo;6C8cME&Lstjx$~vQa zVM&IMTGg#;>N-i-PEL{3cnl0FgQL3a!KCJur_3*?=~wor%%?2O(V-n*vx8sVEMIc^^5T_5aWfHFUlk&7%Z zFA38x%NBzIAB!n}sbmZ1E@{#fzc<1KCasQW0ZP0ah%{-kQ?tyi+}N$!>+AuW+E5{R zOFlx9g@_ay<54?~r{Rbu*iLrj)ps75W~!t>nbF&rz*BytCAqYIcKq$)qjtI5{MWN8dI-w7Z6BXSy|Lq`64v@b92bTC{L! z?2Kz?$~?+Unk6>eFgCMv^XP`qv{v7o*T=0rJHElVMvChH-}hN}4^uY}FE>jo6i!Zl PE^Zza8X74TX_Ws0$DR^p delta 10933 zcmai)RZtw!x`kmT!QI{69R>}q!QI{6eSkrO>kxuV@Zb`HyF-uw!8N$MUQXR}pYPkZ zR7Md5e*VE1|2 z1^X{J{ZVW$I+FHz8C&iOzJjQ3|0Y=I*F#Hv2n|N#d5BZOU^1e5n2Y@C+;U=$9l0hF zK2%I1_8k>-rg+F0Up7NZH(3sE)n(PW!6@3$F#SOXNf?W3x1qSeRUM~k(^G^4F$H3C_ETY|R`xTf=|&A}?5u8gdOWT~zFKXa9Q&$((MD?gXIYX;nxPnR7Tk|W#Joljd< zzth-J3UDfs;Wkk!S4v_2Y%};#6Po_Qr(DO(#xg9;B~c#du4b0$*rfD_CGdWr*9NR# zMT&>a1fy@(u#4L`*&2!)qtU%n(Snp|*0LND+30cejm^Cltm}E=j~(pPoXe?IlL3NI zJN3ikUvQV>k!=M#8gz9uhZJey@AQ6RBN_nIa;mZHnni5o@0>I*uLgYeHDlo$&Q>jS zrj7yMdq25?$=O-jKAl_q@>juSJpku9)MAw~%a^4S!nv0#nBw}9CU=xdJVn3=qpX>Y z=W_5G#FvFoXEgj=ViWA=F;10kfic`)E9_$aTokR3kmS-6avF99?dW_dzGsHVVE=>)I+Lc|+D_3e>8cd7S-b@~L z0y78WdNeWCee-J8Wdip_>sgqG$G6u4ZQlph{8RIq;~7Tl=2vs!4gHYS9M2X$wIl}L zQiLdkc~=D*e7$ZB$8b9r+;6U4m}ma|ABIB2Ky6~6i{h$I*e|En^Q--(+q=uVL_yX> z_3`{Vif7A?9cM_XC12Z#kHIzwbz3DSm=nNmBVrO-rM=$}SPR@f#6Z$lvW!`qF&cU^hpShGS>ay0{!M24ueYKxgF!<_C+YL2zUE;o}*?Z`yqK zUx}`t>y~xRtHvoiR=j=%oe^dH^6qlc5XD&iB8OH?Fd5j^w(PS+9lP)8oE*;w(hnZr zMYwk^^KYNp%uJ5n_b?ZJvWt&vd+c02?a`{zS8{4CFOD*E z^7q%1Z(VjHG9sU7@gMN+H55~P*ECq^^b@+>Vlz)wqZAt6Q|TvwH>6oyuNJGCbU%v# zpOmwxWQ3KV>4%IZd+cu_Pik_0BMEO&BWlcLG;RlF9^)$pmWcxd;&TrEQdAF_4sN~{ zDUJAHbG+K6leXq)X&$x!Q5@L=$jB_R92c^Mp=1P% zV?For@VPm~*Js@z3n!$wQIRF-KE&0d7pt|aZFT2SUnP0{#uuOwwbh^wxz3S(jj%Um6Dwx zt#0WT^GGqTFrg&UD8Wstm4Q00Qwn$Y(Rz{$4;?X6&r8M^u86;%TY=J}MlEN-eQCVL zSqC5GMHAj^(jPZwD6*=0Ykj_@5f1q|Cnc&R_ubId`@VrOGF#ZrEsk!pzmu(T4bJKCa>C-aFAfg$eP0a}I)t)b2*1 zhnoJ9_xS@JkRr)6m4xn-Se)ZT?lDdda|W9z|4b*dgGK(ZWB)aC*@*ivtO+@GNu;z# zie?}%_n%S2%_Um+wvNo$@H7gYCHVavQ&ceZ#c-W2`9+f}dH`^57;Ga3@VeD1XnXoV z-ZI7R&Cu>2$lS-y&HGZAf+EqqImG7yFZ|bF@;0#76YaIh#bJd3yJQoL7@k|}@LfHP zAsgjr-YB>@6+?Aix_CJ;UA_guF3)^fBU5`DhkX|pYZZ$l#qUO}=639)Z2+c3Q=|f0 zaY=}LL8Rdj7_Gs%R)ZmdGpgFkZ~+V`Jv!a|1C{ml>T;qqmr2oj{%~u#>io;9z;>h4 z_yaf{gVMaFdNHrD^I|1#SRJu2A%kMI#_F!G=S4{Yqu_AZ^>1GHM>)bR&6^>?<@kLfPk} zFVq<8E8Nf+z6h9A#MQ3UqfWB19j%uXG}eHH4qB&1<3GPtkg%A>k8k2ZQp@|}Qunl2 zGm}l~*Gn!v-xye+VFq(aoQ%DOaR4Jb?Q_~7nQNnHN|XvSW4GgtT1AfD(zs`RQz;TI zbq-S*-qQ^|Gi8TJ^7%OGu-l}-&aQztaZp;0MId)*$ zJWM3kB#~3(tcSl-`XNYZusHlba{ukm>du6IRprJJrbx%`g}rJqd{*v#Xv(%ghz=Wy zpsvldx~1xsx3KEPg#RPFNT*j2GNRHMq)g5hZ=c`cD89wZ$m*{TY?v0ujsv4qVhd=&$~275q7 zkmf0(wqO!%b)#*~W)}K_2)(TjHc2BAjBb4BNZbtLkbP8YxmetM_51v5K{VyGGmjtr z48lzLkoZ+a?R2Yg=D5X_3F$a2OT6>B^oBPu3MemygwAMkx<9}Q^<=4Z!0cDw0a9Ek zJ=l}rM|q~B-Chg3ac>)Hx&6UutSh1Us*1vSHD<+_7Ur(CshROMOw;Z?A%0bqojAqT z`CD-KjGzxbd&^&5;V32nWE4S_&0~ia<_vidp%44#wRt<>H&%pDB#9+#8_e+sVcu`M zVkOUw$#Qltp@>ZVR#{>M6>$PcLdf!I{f474{|5GWw0WxPbS7UMoAbaAPB9O)sXk$T z!(P$6P_s^Qhw(u4sqwEe@LZSV)C;`c$~BeuF0S7Rb}v{$ZpuKefpaOnEbi5hwNGd_3h1)afFoOf-u5vg8e6^RqJE`>$q#)n_^u@WZjPn)hjge#a;;JRlr72=vP`F1fKYMWb~-aDnK_ ztONW<5o03zEF%r}uFeT(<1J(Cr-O3G{%QW)kqN{rR8iVJ&;+ksJSJ^M!MpJyz(iuS z+CT5L77)0^SpMM*>DPih(an5XbfF;MQO&BUsN{#g#8&+%v~qPj|AdY0lfYfTsJ4Eg zs6IZsE|(r1Nkfyk3DROq9CqY(T^{4YN8}R5gL@Taf@5b6Z$U;qD>aRQ+xuXP9N)ka z@t(IX<|r5~0b}?&!CBjctA-Egl_e$ZhMquXyRmlcoV6ryqC64%VTruHvm{8RM~`l0 zs_$;uQngHUpJHnAB%L7Ji@PG?5vBMK^f-~i%50;{Ed8Sb3h;c%`6NRl7#e3*2DC(J zpB(NH6iytlVnb2N#l1bDjJG})6F~^y^q--R{^lNv2u?ItwdHcC#kD7NCN!N{is=BvV;M|rBu0Qt_g6PYTyM#*e5F{8JIQcJai+fS2H1tepRcQ;W%$VE~ zhY3jC#fwl+i#U>-+#0?o(I^!(!&MZ-3LOM6I(!#diQ|-;Y|Qa?P2}oFz9Qke-s1S0 z9c^lEriR-=XMMhbVmUXryJr<*Bum?djkr|P?+wN*&fxe4fI*|YT1iqiClrqC&UPQxkTMzEPg#hahQxt=3o zssO2Ipjt*O{sm`L2sFbpiWO8y-Qa4LH0Yply$PBz>1g37>uGqrkvd=;;-9WVfv6I= zlHl|O(+4JkYRujz6Gevk&GQKB)`=yCbpXtGPannA(w7!C{!w@Z6I;%Pk6|bel<-V~)5+EnO3)@cF=$DQ?x2@M? z6Mo%1NmwOFO2-4Qod|AHQtyr>JhbTIER|eVxA0LPL8yLKE=P>n2R6K0ENJA4g&{z1BT5bY6XI)o8z zq#f;qO2e+gc1=shg4K$5;--csp3H<9)HJ?jO4C2*MvqWV_ArrUNMw|zg7Y~xV zshAVm9qe{k%Q8VL%BTq03h1~y2SdOPZ|m2x+@gt!_<@jKbLN>6Pv+Ec;a9#I6u(&P9Gq7PKP@EcAyq1VFSVdCk;>^3divmcc zhPs};V>}0-jRrc60>EuC)Bcr9GP09sXBH04#S4EDI0;2o0kKVz-d618)G(RyrUy^c@>o7Px@o0O&0P z5C>{1@UGW+fldJE8#556aWm?e1{-X(b-=nYM zKuRF=vj9*J`tCZl>`DWj0nkvP_bF}V-baHri@tZ~DFS1{T+rhXwrM@I^~tnaheS%wcM27~x>XFbqS*3TSjg%ED(9P7%%-)8-qo zy0tLofbDo0b8(1&KYSi*h=gH1=ft&>VwlOGRX^vH(Ut-u`zvFTSZA7EqlM~i%D3$^ zEW)4wwM`LmNRi{HZK1bUA2l-k-G+xJKebbQ6PDZQUxmV%Rl)49SLDKLjO%Z$ zRk4>7_f>0*dE+*f{>}P$xf|Z2J~!^cO#ndeNM?yS?>Tc3e1$zscbvzN|8$ z&z(RPWF`7AL_yYRwx@%ZsoM7BNUDw`YSg1VqtD>dE|-uwl!I&n@g34(K$`Nu*zK_k z`FPd=jkP$PN`Fpf%l4qhpqpb~UgP=25T05MvXGx)AKYOaC1~W65@yqYj(W+pq)7$) zaFI%t2dQp6=Z?&EF7i(0Q(tUNb&twxh84=t`9}F;A4c3dm^wplUm%5nCSVg>2R*|| zyaVu~fASvM7e*hO2GDd6Wt9BRwf63i(C)?j0`5BbXKV0rTENwSU5DxO*4<@opt0zK z#ENDYwm7}1)L)JY6hC$$s$X8#I~!lLc#-}9>|6Giw!6@}CjK$AXeahlV<|WwT;B4f zLi|P4UEO;}lP_-Hzx`6hcVv=?;Uls*R0F{a6dSo(Uhx;ZaB0MNa9R*}xw*f(xDO2h z1Q|q*zE)>8y2&I~WOJQyMBBw-9p^mSn*CJqa zU#nFj2v_<#0{H`UfB7gjZNer7vkuL`QM%r4W}d}oAziTNS;*qG+N zDv2(0cVoKKk)45weo(D>P9597Y8%0f1^o1EVlYj@Y+TNYs4TV@atL&CHCC>Qf) z(h_XVm(%J)3{Cnv{bFIdj3e#mcY6YMce`!6uixufsd>xFo;%AuaZ7lXcHj;xN8${d z?95Li@iXMDV0xTx-N>yt9=5W$=p;>#JogQKV8Ggy1H@Vli^tOUP$dL%V#JFBP+rrC z3(Dr^EY84^ zZyHB0#H~s((z7>&sU8OCaIR37Ru<2tgS))Pn??E6Vei|SDLL1yVp%l4=GqsWWX3vP zNUPHFSb=+T6Ozgl*X60b!cTEK+2SF-gj$eRuI(2`y)7!D7~cNO*j_Nu5X)|mzWFnz z?$0>-go~AMBfYGiZ@ioQYT1P;N4pm>Pfb>h>tj;g!zq0A!QVy5PWCmM1yY!l@C79p zj=hgBy6+1m>PwSD7ZX`)lyW~d5qV2?SxpUAQ^J;J45a^6BK0Ho(RaLZOP?j9#aixu zjaz28q`8m#Lt?YWM`R1e?b}kqAHs@p5*=eonXJ8GIWuD}Jf9tCXx31)G4fQfk*DHs z$@Oyo#@9o?a>QG|h;i~Mn!vqqQLolcuD{!3+h_p0P&SUiy@tzCnrEIS;?$kru$Q-C zv1RWU1^L0Ex-(Gk+t^K;Tt?=R@eJD3cYF8vlc=~HpsXV*JS97L1f=*u|ARYPP91sP zT4}uRCEpJ#CO%!~?dWZevyI=ipsJ!zz4axZQC09Yxe!w+aN&6&o*%zMc3{LYa+3k2 zG-pE`h};%(LF~5L`TbNsQvU2}Yl?fqvB>Ti67&VjYQ_m1@E$RbBy&LIdlR;ssm^4n zaqhURXw0k>MxR>1cGA*OlB78+!I#ylrDJ>a4}VwbbIMoi7#t_Ct$4WFRx*jfMgk`JUAYIK}Fqv znw~K$6i(9PMR;3oT?(-xr897kCJ6Nh@isEXG>sGU(d-6-9XoNC>4^O&PiiN2TR6X1 zeHqE=b-j`m{y86Tu8_=ocfh7-c{*#Y_fhtm;Navh>98^wJL4$Gde-yL*i7C&5B8oT zO?BqPA$>R|TVz;v{iM=TWZkAha_#F3MtvcUNKlq1bWpR+In}S?Skm_r=dXOTl%Q!i zp_XBzR96KE95n41$=1Ut%WCzFhfP=d3o;B*B1g91Uj%XXy~ROLk&||;)9^njriu*y z`J$Z1&q@xD74~Pu0&UQHUu9|oW4|98y%36IYT`iKIlknX3vMQTOq)+0wT4N8Ys!s1 zr{zWHy>O8}`Lj!kjQM4OEnXMo&iiNuj*)yfW zk(HU?HBmxb$_2=Ori}1WDk+vkMN=h_S2K;>)7^`NL@)o+_XauOpMQFN@@HR8;5#xp zN?CqtCuqgf6ilVyPop5Yx8Th9X*hdT4@w@<1H%gn7u+k3w3g&g4yl)q<5)Jq{lY$S z4Kr(P!c4SM*$2YEeo+n=&MR#Fgqw$YVHhVLAynWZ&JmhbD4gT&$471QfgFF^esT~9 z^D>LXg0Ek}3wI)jV+l{ZN*yQA72jt_n#`RR$kacC_Pr3bGJWeyHkKN=UIb5Mj!!%yf_v$ac8vV8AYMhc1S{sFtGolsMjI&?d z7K>*F?A5hgcf6yjJugy~8%|gG?&VG0hRY_iC%r?;vnW$%Bbb)dFi(*O?4~)!!4yk zLpE*B*yVWUXN$zr*>X6O?60m@4{Rf%n{*71>S|g`H}RX>>lvHQH67GEYNSr=I@Iya z6(y)U54loP+<#Or^olW2zm`B0ajnw|`%rqNR$*fNgm6^n}atTd#FDqh(Uo!0C`TN`76rNtc`n;XjG4KcK zKUZPN7S(4K1%_J<;-lDZ*fm?UtAtf-c)=0&I3`i_)Ig^0Bn81>ROhU_BVLepd zV_TrBDViGRRf?N`XoLgj&w*iz@2;p$|FbzI+2xRC=%MiBA;|m`OGGZ;Ta7N_h9&Vo4v<`X({WUHE&YaM0>cy^^2uNtCx6QrwD8+gg$@syIb zwH=2U8p(txKB^;$JPLwh`GqHaVjm9XM-Dyf+p`nEY2f*FottA%5G9fa;iEk|7-RQtJMIRPXpPdcs4bU4C-Rd*O$jGV3 z!egbZv(TKcZ4Nl^;w9YP<#kybKcgClW?~llGsNDC&HH{oYjU={?l^Awd_@l&k=M+be>CW%dN&Y^$7M}BfU zwNeY!PDAdY$hf)>`BCjtapXZ@v-aRYpfsI8s5baetY&alhW{GA=~>5<=WA|r)}!&O z#;XSV9;uhp?y=Z$*JJCiu|s#_xsok5ge7R$^E$PtLXV1HAN~Y`$1;PtYFK3a5B@GH+jyPc zz}d;&_%`p7m-rZt`goo-(xBJ-XP6lQ(Y58ws$X7Ico>Dxs8|Kd%bE;K_%Rno$-+^p z%74B!Fe>|>+J79nR)Jnr8_rz$z{~#X!rBIRIaR4iTx2TZh})D+Hahk(oo2+VIyLm* zyd#J5nu=4Z;$QT8yhQG>!i&otKBMr(;6Nf+q1@PIFoZs{xsC+P*lZG^)ss$=#zl+ zl$ArQ)WF~VtV4B7pdot7Y;+n)e!LJp_Ka;i9SsA}LSM%}74-G`?|i;G;g6r*oGWO) zmIlFye4X&Zh%FzR)K0iLIZa(~G3F5ZMuHJ0ozK2D`_?FkPu6?N_bdM*rFs4`G4|px z&`JEOTdfuit>=Xt2UA*1v!ey{l(_lELI(CEz&7xkZc(|r z3tml(8~H|slyk0mSU|8$@^%NRKq0jqeGNX89ncQ;d^@O_5*2ya-Sxe23x3`<@56)^ z6(NbQm&;&Vo+_k|(ssARf8fixjb6#BRCf1~f;5aASB=eRquHFj%=SSbCdOd0vyK(Z zip88n-W0*|Mu6B?nWhsvp6Bd5Wlf5S=I3@+G3f8onK#lG5Niz^R6}5!Ex-Vj@563# z{BrvM-90pKzpslCr(~o=AH2f%I(QS*$CIAFkT_1$FT(Z4{^st17@=;f)Q$7|Pz=-E zx{@u5IPmjrq6rT|cEGmP#2XlnSHS-SAv{Kq5s?>Q51EK{K3iQVS!v{T*~!5{PW#QU8_=C8byj1ES7Z?N;5XQZBk%M;FEQ6O z;3Aq5WF6q{4{u=P-rJqY=x+4u=P~c!`sLJFA&kT1qTu=k11pdS&5)Cd@>zG0>|}R_ z(~!56%p`BX3)+v`0MXw?)~2I^mUEd(TJuSnwIZCWsS#wHn}7OIa7#`%(tee~8kz5x zx;)N#X1nhixJQ07Tx8=lcd@1UBidJso`!(0;BS^Md?rw+aLy~__9G^ z&9!?4S86`4<1Z_nD%0J8nm_832&Z`gZ4etWy6vDZaC|!+U%-Li>m3~T(N6tzr*9aE zB5MroJZFb(GX;(u0(o9s`%{8JTS!OLSe=>KY~R+i6uQXLg4t_gH3dG z$bc500I>l){LtqBASIYbzzB(5!_MD|f|Ex8iCu@nfRloog7e)}cX9E2H+d;IDAbYI z<(;iv-WA_}l@x`6uoQ<32S@@Wz#}6i#mmDh!^tfL;@}hKkmiu&HrzRq%&PE6J|I=7grC#%f^5085Ld_ydK<}3>(?14W#WDt1~jxTTZry zDC&4$VVK3+yz7$)`YHGf_*3QZQ;U=3GNYplCZAYp+VggVr}W6U8`Ar$+CDaSYjcz| zB*tNBj#P0bAQroRlre>g+yod##JZBwnE?h(k?ix)v?ZIsRo;}jQ#}+b;cB`cp&P<; zefnkTO=;VIi3p;`rePNHG5_=l>S=%3q-%whti|N(gVQ^ZjN|E}TZCIK!1eA{wuKla zMXlDtb1fo2<-ZuVS&xTGq`o-d#2Gm5lsrfZZEx ZnWA_h)F~K9hRpZA-bl2x(ke1Y{{#F(tfK$` diff --git a/Secondo anno/Algebra 1/3. Teoria delle estensioni di campo e di Galois/4. Il teorema dell'elemento primitivo e di corrispondenza di Galois/main.tex b/Secondo anno/Algebra 1/3. Teoria delle estensioni di campo e di Galois/4. Il teorema dell'elemento primitivo e di corrispondenza di Galois/main.tex index 1cc1730..84866ba 100644 --- a/Secondo anno/Algebra 1/3. Teoria delle estensioni di campo e di Galois/4. Il teorema dell'elemento primitivo e di corrispondenza di Galois/main.tex +++ b/Secondo anno/Algebra 1/3. Teoria delle estensioni di campo e di Galois/4. Il teorema dell'elemento primitivo e di corrispondenza di Galois/main.tex @@ -306,10 +306,14 @@ $\QQ$. In particolare vale che: \[ \mu_\alpha(x) = \prod_{i=0}^1 \prod_{j=0}^1 (x + (-1)^i \sqrt{2} + (-1)^j \sqrt{3}) = x^4 - 10x^2 + 1. \] + In modo analogo si ottengono i polinomi minimi + di $\sqrt{2} + \sqrt{3}$ su $\QQ(\sqrt2)$, + $\QQ(\sqrt3)$ e $\QQ(\sqrt6)$, rispettivamente + $x^2-2\sqrt{2}x-1 = (x-\sqrt{2})^2 - 3$, + $x^2-2\sqrt{3}x-1 = (x-\sqrt{3})^2 - 2$ e + $x^2-(\sqrt{2} + \sqrt{3})^2 = x^2 - 2\sqrt{6} - 5$. Tutte le informazioni sono infine raccolte nel seguente - diagramma di estensioni: %TODO: terminare esempio - - + diagramma di estensioni: \[\begin{tikzcd}[column sep=2.25em] && {\overbrace{\mathbb{Q}(\sqrt{2}, \sqrt{3})}^{\mathbb{Q}(\sqrt{2} + \sqrt3)}} \\ \\ @@ -326,9 +330,25 @@ \arrow["{x^2-3}", curve={height=-12pt}, no head, from=3-5, to=5-3] \arrow["{x^2-2}"', curve={height=12pt}, no head, from=3-1, to=5-3] \arrow["{x^2-6}"'{pos=0.3}, shift left, curve={height=12pt}, no head, from=3-3, to=5-3] - \arrow["{x^2+2\sqrt3\,x+1}", curve={height=-18pt}, no head, from=1-3, to=3-5] - \arrow["{x^2+2\sqrt2\,x-1}"', curve={height=18pt}, no head, from=1-3, to=3-1] + \arrow["{x^2-2\sqrt3\,x+1}", curve={height=-18pt}, no head, from=1-3, to=3-5] + \arrow["{x^2-2\sqrt2\,x-1}"', curve={height=18pt}, no head, from=1-3, to=3-1] \arrow["{\small x^2-2\sqrt6-5}"'{pos=0.8}, curve={height=12pt}, no head, from=1-3, to=3-3] \end{tikzcd}\] + Tramite la corrispondenza di Galois abbiamo fatto + corrispondere questo diagramma al seguente diagramma + di gruppi: + \[\begin{tikzcd} + & {\{ \text{Id}_L \equiv \varphi_{00} \}} \\ + \\ + {\{ \varphi_{00}, \varphi_{01} \}} & {\{ \varphi_{00}, \varphi_{11} \}} & {\{\varphi_{00}, \varphi_{10}\}} \\ + \\ + & {\{\varphi_{01}, \varphi_{10}, \varphi_{01}, \varphi_{11}\}} + \arrow[no head, from=1-2, to=3-2] + \arrow[no head, from=1-2, to=3-1] + \arrow[no head, from=1-2, to=3-3] + \arrow[no head, from=3-2, to=5-2] + \arrow[no head, from=3-3, to=5-2] + \arrow[no head, from=3-1, to=5-2] + \end{tikzcd}\] \end{example} \end{document} \ No newline at end of file