Isomorphism yog homomorphism tshwj xeeb. Greek keeb kwm "homo" thiab "morph" ua ke txhais tau tias "zoo tib yam." Muaj ob qhov xwm txheej uas homomorphisms tshwm sim: thaum ib pab pawg yog ib pawg ntawm lwm pawg; thaum ib pab yog quotient ntawm lwm tus. Qhov sib thooj homomorphisms hu ua embeddings thiab quotient maps.
YPuas homomorphism txhais tias isomorphism?
Hauv algebra, homomorphism yog daim ntawv qhia kev khaws cia ntawm ob lub algebraic ntawm tib hom (xws li ob pawg, ob lub nplhaib, lossis ob qhov chaw vector). … Ib homomorphism kuj yog ib qho isomorphism, endomorphism, ib qho automorphism, thiab lwm yam.
homomorphism thiab isomorphism ntawm pawg yog dab tsi?
Isomorphism. Apab pawg homomorphism uas yog bijective; i.e., txhaj tshuaj thiab ua tiav. Nws inverse kuj yog ib pawg homomorphism. Hauv qhov no, pawg G thiab H yog hu ua isomorphic; lawv txawv tsuas yog cov cim ntawm lawv cov ntsiab lus thiab zoo ib yam rau txhua lub hom phiaj siv tau.
Homomorphism hauv pawg ntseeg yog dab tsi?
Ib pawg homomorphism yog daim ntawv qhia ntawm ob pawg xws li pab pawg ua haujlwm tau khaws cia: rau txhua tus, qhov khoom ntawm sab laug sab yog nyob rau hauv thiab sab xis -txoj sab hauv.
homomorphism nrog piv txwv yog dab tsi?
Piv txwv 1:
Cia G={1, –1, i, –i}, uas tsim ib pab pawg nyob rau hauv kev sib faib thiab I=pawg ntawm tag nrho cov integers nyob rau hauvNtxiv mus, ua pov thawj tias daim duab qhia f ntawm kuv mus rau G xws li f(x)=in∀n∈I yog homomorphism. Li no f yog homomorphism.
