abelian vistaar

amoort beejganit mein, ack abelian vistaar ack gallois vistaar haye jiska gallois samooh abelian haye. jaba gallois samooh bhee chakreeya hotaa haye, tou vistaar koo chakreeya vistaar bhee kahaa jaataa haye. doosari disha mein jaane parr, ack gallois vistaar koo hull karane yogya kahaa jaataa haye yadi iska gallois samooh hull karane yogya haye, i.ee.yadi samooh koo ack abelian samooh key samanya vistaaron kii ack shrinkhala mein vighatit kiya jaa sakata haye. ack seemit kshetra kaa pratyek seemit vistaar ack chakreeya vistaar haye.
varnan.
varg kshetra siddhant sankhya kshetron key abelian vistaar, seemit kshetron parr beejganitiya vakron key kaary kshetron aur sthaaniya kshetron key baare mein vistrit jaankaari pradaan kartaa haye.
cyclotomic extension shabd kii dou alag-alag paribhaashaaen hain. iska arth yaa tou kissy kshetra mein ekataa kii sannihit jadon dwara gathit ack vistaar hoe sakata haye, yaa iss tarah key vistaar kaa upa-vistaar hoe sakata haye. cyclotomic kshetra udaaharan hain. donon paribhashaon key tahat ack cyclotomic vistaar hamesha abelian hotaa haye.
yadi kissy kshetra "key" mein ack adim "aine"-th mool ekataa haye aur "key" key tatva kaa "aine"-th mool sanlagn haye, tou parinami kumer vistaar ack abelian vistaar haye (yadi "key" mein visheshta "pee" haye tou hamein kahana chaahiye kii "pee" "aine" koo vibhajit naheen kartaa haye, kyonki anyatha yeh ack alag karane yogya vistaar honey mein bhee whiffle hoe sakata haye). halanki, samanya roop seey, tatvon kii "aine"-veen jadon key gallois samooh "aine"-veen jadon aur ekataa kii jadon donon parr kaam karate hain, joe ack gair-abelian gallois samooh koo ardh-pratyaksh utpaad key roop mein dete hain. kumer siddhant abelian vistaar mamle kaa puuraa vivaran detaa haye, aur kronekar-webber pramey hamein bataata haye kii yadi "k" parimeya sankhyaon kaa kshetra haye, tou ack vistaar abelian haye yadi aur kewal tabhi jaba yeh ekataa key mool seey satey kshetra kaa ack upakshetra haye.
topology mein maulik samooh key saath ack mahatvapurna saadrishya haye, joe ack sthaan key sabhi aavaran sthaanon koo vargeekrit kartaa haih abelian cover koo isake abalionization dwara vargeekrit kiya jaataa haye joe seedhe pahale homology samooh seey sambandhit haye.

