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%EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 1 1 1 0 bop 324 548 a Fg(Mathematisc)m(hes)37 b(Institut)1318 b(WS)37 b(2002/2003)324 668 y(der)g(Univ)m(ersit)972 673 y(\177)973 668 y(at)f(M)1216 673 y(\177)1213 668 y(unc)m(hen)1657 b(Blatt)36 b(1)324 789 y(Prof.)h(Dr.)g(B.)g(P)m (areigis)1664 1287 y Ff(Algebra)45 b(I)443 1515 y Fe(1.)90 b(\(a\))48 b(Zeigen)32 b(Sie,)g(da\031)h Fd(K)i Fe(:=)27 b Fc(Q)40 b Fe(+)22 b Fc(Q)1977 1433 y Fb(p)p 2066 1433 49 4 v 2066 1515 a Fe(2)33 b(ein)f(Un)m(terk)2599 1519 y(\177)2599 1515 y(orp)s(er)i(v)m(on)f Fc(R)43 b Fe(ist.)603 1677 y(\(b\))49 b(Zeigen)32 b(Sie,)g(da\031)h Fc(Q)45 b Fb(\032)28 b Fd(K)40 b Fe(eine)32 b(galoissc)m(he)g(K)2517 1681 y(\177)2517 1677 y(orp)s(ererw)m(eiterung)i(ist.)h(\(5\))443 1881 y(2.)49 b(Zeigen)32 b(Sie:)609 2084 y(\(a\))48 b(Der)40 b(v)m(on)h(1,)1314 2038 y Fa(3)1289 2002 y Fb(p)p 1372 2002 V 82 x Fe(2)f(und)1691 2038 y Fa(3)1666 2002 y Fb(p)p 1749 2002 V 82 x Fe(4)g(aufgespann)m(te)i Fc(Q)11 b Fe(-Un)m(terraum)46 b Fd(L)40 b Fe(v)m(on)h Fc(R)51 b Fe(ist)782 2204 y(sogar)33 b(ein)f(Un)m(terring)g(v)m(on)h Fc(R)5 b Fe(.)603 2366 y(\(b\))49 b(F)849 2370 y(\177)846 2366 y(ur)33 b(ein)f(v)m(on)h(Null)e (v)m(ersc)m(hiedenes)36 b(Elemen)m(t)c Fd(x)c Fb(2)h Fd(L)j Fe(ist)g(die)h(Abbildung)1850 2586 y Fd(L)28 b Fb(!)f Fd(L;)17 b(y)31 b Fb(7!)c Fd(xy)782 2806 y Fe(ein)32 b(injektiv)m(er)h(V)-8 b(ektorraumhomomorphism)m(us.)614 2968 y(\(c\))49 b Fd(L)33 b Fe(ist)f(sogar)g(ein)h(K)1506 2972 y(\177)1506 2968 y(orp)s(er.)1679 b(\(5\))443 3172 y(3.)90 b(\(a\))48 b(Seien)33 b Fc(Q)46 b Fb(\032)28 b Fd(K)40 b Fe(und)33 b Fc(Q)46 b Fb(\032)29 b Fd(L)k Fe(K)1953 3176 y(\177)1953 3172 y(orp)s(ererw)m(eiterungen.)h(W)-8 b(enn)33 b Fd(\033)f Fe(:)c Fd(K)36 b Fb(!)27 b Fd(L)782 3292 y Fe(ein)39 b(K)1022 3296 y(\177)1022 3292 y(orp)s(erhomomorphism) m(us)e(ist,)i(dann)g(ist)g Fd(\033)k Fe(sogar)c(ein)f Fc(Q)12 b Fe(-K)3299 3296 y(\177)3299 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