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Fc(1)1125 1622 y Fi(und)g Fh(G)1403 1637 y Fc(2)1479 1622 y Fi(zyklisc)m(h)g(v)m(on)f(der)g(Ordn)m(ung)g Fh(p)g Fi(ist)f(und)h(geb)s(e)g(jew)m(eils)782 1742 y(ein)32 b(erzeugendes)j(Elemen)m(t)e(dess)h(Zen)m(trums)f(an.)603 1904 y(\(d\))49 b(Man)42 b(en)m(tsc)m(heide,)i(ob)e(die)f(Gleic)m(h)m (ung)g Fh(g)2346 1868 y Fd(p)2429 1904 y Fi(=)i(1)e(f)2671 1908 y(\177)2668 1904 y(ur)h(alle)e(Elemen)m(te)i(der)782 2024 y(Grupp)s(e)33 b Fh(G)1215 2039 y Fc(1)1287 2024 y Fi(bzw.)g(f)1547 2028 y(\177)1544 2024 y(ur)g(alle)e(Elemen)m(te)h (der)h(Grupp)s(e)g Fh(G)2875 2039 y Fc(2)2947 2024 y Fi(gilt.)320 b(\(6\))443 2228 y(8.)49 b(Sei)32 b Fh(R)h Fi(ein)f(Ring.)f(Zeigen)h(Sie,)g(da\031)g(folgende)f(Bedingungen)2892 2232 y(\177)2892 2228 y(aquiv)-5 b(alen)m(t)32 b(sind:)609 2431 y(\(a\))48 b(Jede)41 b(Menge)g(v)m(on)f(Linksidealen)g(v)m(on)g Fh(R)h Fi(en)m(th)2586 2435 y(\177)2586 2431 y(alt)e(ein)h(maximales)d (Ele-)782 2552 y(men)m(t.)603 2713 y(\(b\))49 b(Jede)34 b(aufsteigende)f(Kette)f Fh(I)1875 2728 y Fc(1)1943 2713 y Fg(\032)c Fh(I)2091 2728 y Fc(2)2158 2713 y Fg(\032)g Fh(I)2306 2728 y Fc(3)2373 2713 y Fg(\032)g Fh(:)17 b(:)g(:)32 b Fi(v)m(on)h(Linksidealen)f(wird)782 2834 y(station)1076 2838 y(\177)1076 2834 y(ar,)g(d.)h(h.)f(es)i(gibt)d(einen)i(Index)h Fh(n)f Fi(mit)e(der)i(Eigensc)m(haft)1693 3054 y Fh(I)1736 3069 y Fd(n)1810 3054 y Fi(=)28 b Fh(I)1957 3069 y Fd(n)p Fc(+1)2122 3054 y Fi(=)f Fh(I)2268 3069 y Fd(n)p Fc(+2)2433 3054 y Fi(=)h Fh(:)17 b(:)g(:)614 3295 y Fi(\(c\))49 b(Jedes)26 b(Linksideal)d(v)m(on)i Fh(R)g Fi(wird)f(v)m(on)g(endlic)m (h)g(vielen)g(Elemen)m(ten)h(erzeugt.)568 3498 y(In)33 b(diesem)f(F)-8 b(all)30 b(wird)i Fh(R)i Fi(linksno)s(ethersc)m(h)f (genann)m(t.)855 b(\(4\))324 3726 y(Abgab)s(e:)32 b(Dienstag,)g (21.4.2003,)f(11.00)h(Uhr,)2088 3705 y(\177)2076 3726 y(Ubungsk)2449 3730 y(\177)2449 3726 y(asten)i(im)d(1.)h(Sto)s(c)m(k)i (des)f(Ma-)324 3847 y(thematisc)m(hen)g(Instituts.)324 3967 y(Bitte)f(geb)s(en)h(Sie)f(auf)g(Ihrer)h(L)1475 3971 y(\177)1475 3967 y(osung)g(Ihren)h(Namen)e(und)h(Ihre)2753 3946 y(\177)2741 3967 y(Ubungsgrupp)s(e)h(an.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF