levitskyude sidhaantham

ganithashaasthrathil, kooduthal vyakthamaayi ring sidhaanthavum nill idealukalude sidhaanthavum, jacob levitskyude peril peritta levitskyude sidhaantham, oru valath notherian valayathil, oro nill vann-sided idealum nilpottant aayirikkanamenn prasthaavikkunnu. kothe anumaanathinte aadhikaarikatha soochippikkunna niravadhi phalangalil onnaanu levitskyude sidhaantham, koodaathe kotheyude chodyangalilonninu yadhaarthathil oru pariharam nalki. phalam aadyam 1939 ll samarppikkukayum prathyekichu lalithamaaya oru thelivu nalkukayum cheythu.
thelivu.
ithil kaanappedunnathupole ithu uttumiyude vaadamaanu 
a" "r" ll ulla formula _ 1-nte aneehilettarukalile aarohana shringhala vyavasthaye "r" thripthippeduthunnuvennu karuthuka. appol
r" oru sariyaaya notherian valayamayirikkatte. appol "r"-nte oro poojyavum ekapaksheeyamaaya idealum nilpottant aanu. eee saahacharyathil, mukalilum thaazheyumulla nilraadikalukal thulyamaanu, koodaathe eee ideal nilpottant raitt idealukalkkidayilum nilpottant lephtt idealukalkkidayilum ettavum valia nilpottant idealaanu.
"proof": muun lemma kanakkiledukkumbol, "r" nte thaazhathe nilradical nilpottant aanennu kaanikkan ithu mathiyakum. r" ennathu notherian aayathinal, oru maximal nilpottant ideal "n" nilavilundu. n" nte paramavadhi anusarichu, "r"/"n" enna koshant ringinu poojyamallaatha nilpottant idealukalilla, athinaal "r"/"n" oru semiprime ring aanu. thalphalamaayi, "n" ll "r" ennathinte thaazhnna nilradical adangiyirikkunnu. thaazhnna nilradicalil ellah nilpottant idealukalum adangiyirikkunnathinaal, athil "n" umm adangiyirikkunnu, athinaal "n" thaazhnna nilradicalinu thulyamaanu. kyu.iii.dii.

