Vim yog ib qho isomorphism khaws cia qee yam qauv ntawm pawg lossis pawg lej, nws feem ntau siv los qhia cov teeb meem nyuaj rau ib qho yooj yim lossis zoo dua-paub teeb kom tsim tau cov khoom qub. Isomorphisms yog ib yam ntawm cov kev kawm nyob rau hauv pab pawg neeg txoj kev xav.
Yuav ua li cas isomorphism?
Nyob rau hauv paub daws teeb meem algebra, ib pab pawg isomorphism yog ua haujlwm ntawm ob pawg uas teeb tsa ib-rau-ib tsab ntawv sib tham ntawm cov ntsiab lus ntawm pawg hauv txoj hauv kev uas hwm cov haujlwm ua haujlwm pab pawg Yog tias muaj ib qho isomorphism ntawm ob pawg, ces cov pab pawg hu ua isomorphic.
Dab tsi ua rau isomorphism?
Definition 1 (Isomorphism of vector spaces). Ob qhov chaw vector V thiab W hla tib daim teb F yog isomorphic yog muaj qhov bijection T: V → W uas khaws cia qhov sib ntxiv thiab ntsuas qhov sib npaug, uas yog, rau tag nrho cov vectors u thiab v hauv V, and all scalar c∈ F, T(u + v)=T(u) + T(v) and T(cv)=cT(v).
Dab tsi yog qhov zoo ntawm isomorphism ntawm ob pawg?
Pab muaj ntau yam khoom lossis cov yam ntxwv uas tau khaws cia hauv isomorphismIb qho isomorphism khaws cov khoom zoo li kev txiav txim ntawm pab pawg, txawm tias pab pawg yog abelian lossis tsis yog abelian, tus naj npawb ntawm Cov ntsiab lus ntawm txhua qhov kev txiav txim, thiab lwm yam. Ob pawg uas txawv ntawm ib qho ntawm cov khoom no tsis yog isomorphic.
Yuav ua li cas yog isomorphism?
Theorem 1: Yog tias isomorphism tshwm sim ntawm ob pawg, ces tus lej sib raug, piv txwv li yog tias f:G → G′ yog isomorphism thiab e, e′ yog qhov sib txawv ntawm tus kheej. hauv G, G′, ces f(e)=e′.
