
koszul-tashi tharav

ganitat, kozul-tetsche resolution kinwa bhagakar ring "r"/"m" chey kozul-tates complexes heey "r"-module mhanoon tyache projective resolution aahe, jyamadhye "r" varr dg-bijganitachi rachana dekhil aahe, jethe "r" hii eka parivartaneey ring aahe aanee "m" heii "r" haah eka aadarsh aahe. bhagfal "r"/("x" 1,) sathee koszul sankalpache samanyikaran mhanoon teey sadar kele gele..., ghatakanchya niyamit kramane 'r' chaa 'x' n). bii. aar. ess. tii. cohomologychi ganana karnyasathi kozul-tett resolutioncha vapar keela. yaa sankulachya vibhedkala kozul-dett vyutpatti kinwa kozul-dett vibhedak mhanatat.
bandhkam.
pratham sadhepanasathi samaja qee serve ringjamadhye parimey sankhya "q" asatat. samaja, aaplyakade shrenibaddha atiparivartanshil ring "x" aahe, jenekarun
eka vibhedak 'dii' saha,
aanee "x" ± "x" heey eka eksandh chakr aahe ("dx" = 0). mug aapan eka naveen ring tayar karoo shakato
chull "tii" madheel bahupadi, jethe vibhedak "tii" paryant vistarle jaate
(bahupadi ring hii atiarthat samajali jaate, mhanoon jarr 'tii' chee visham degree asel tarr 'tii' 2 = 0.) ghatak 'tii' jodanyacha parinam mhanje 'ex' dware darshavilelya 'ex' chya samarupatechya ghatkala nasht karane aanee 'vaay' ajunahi vyutpattisah eka atiaanvik ring aahe.
aar"/"emm" chey kozul-teteche resolution khalilpramane tayar kele jaau shakate. aapan parivartanatmak ring "r" pasoon suruvat karato (shrenibaddha jenekarun serve ghatakanchi degree 0 asel). nantar samarupatetil aadarsh "m" chey serve ghatak nasht karnyasathi 1 vya anshapeksha varche naveen chull joda. tyanantar sakaratmak patalichya serve samarupata nasht karnyasathi adhikadhik naveen chull (bahudha eka anant sankhya) jodat rahaa. aapan vyutpatti "dii" saha supercommutative shrenibaddha ringsah samapt karato jyache 
samarupata hii fakt "aar"/"emm" aahe.
jarr aapan vaishishtyapurn 0 chya kshetravar kaam karat naslyas, vareel rachana ajunahi karya karate, parantu samanyatah tyateel khaleel bhinnata vaparane adhik changle asate. bahupadi rings 'x' ['t'] vaparnyaivaji, ekhadi vyakti 'vibhajit shaktinsah bahupadi ring' x '′t' vaparu shakate, jyat ghatakancha aadhar aahe.
kuthe?
0 yaa vaishishtyapurn kshetravar,