[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"word-pääideaalialue":3},{"word":4,"glossSources":10,"senses":12,"sensesFi":13,"frequency":8,"etymologies":24,"etymologyFi":8,"etymologyFiLinks":8,"synonymsByPos":25,"extendedSynonymsByPos":26,"antonyms":27,"hypernyms":28,"hyponyms":29,"englishTranslations":30,"wordnetGlosses":31,"fiSynonyms":32,"fiExtendedSynonyms":33,"fiAntonyms":34,"fiExtendedAntonyms":35,"seeAlsoBase":8,"altSpellings":36,"fiBaseWords":37,"fiBaseWordsGuessed":11,"fiDerivedFrom":41,"fiCompounds":42,"fiDerived":43,"fiRelated":44,"wnAttributes":45,"wnCauses":46,"wnVerbGroups":47,"fiTranslations":48,"exampleSentences":49,"inflectionForms":8,"allInflectionForms":8,"rhymePattern":8,"rhymeSamples":55,"categories":56,"domains":57},{"id":5,"lemma":6,"hyphenation":7,"pos":8,"kotusClass":8,"kotusGradation":8,"homonymIndex":8,"ipa":8,"isStub":9},438354,"pääideaalialue","pää­i­de­aa­li­a­lu­e",null,false,{"enWiktionary":9,"fiWiktionary":9,"wordnet":9,"aiGeneratedEn":9,"finnWordNet":9,"psychling":9,"termipankki":11},true,[],[14],{"index":15,"parentIndex":8,"glossFi":16,"glossFiLinks":17,"examplesFi":8,"tags":21,"source":23},0,"kokonaisalue, jonka jokainen ideaali on Matematiikka:pääideaali",[18],{"text":19,"target":20},"Matematiikka:pääideaali","pääideaali",[22],"Matematiikka","termipankki",[],[],[],[],[],[],[],[],[],[],[],[],[],[38,39,40],"pää","ideaali","alue",[],[],[],[],[],[],[],{},[50],{"paragraph":51,"matchedForm":6,"matchOffset":52,"bookId":53,"bookTitle":54,"bookAuthor":8,"bookSlug":8},"Tämä  tarkoittaa  seuraavaa:  Olkoon  annettu  nouseva  jono  ideaaleja  Tällöin  on  olemassa  positiivinen  kokonaisluku ,  jolle  Koska  pääideaalialue  on  rengas,  jossa  jokainen  ideaali  on  yhden  alkion  virittämä,  ovat  Noetherin  renkaat  pääideaalialueiden  yleistyksiä.",140,"https://fi.wikipedia.org/wiki/Noetherin%20rengas","Noetherin rengas",[],[],[]]