{"title":"值域上的关键多项式","authors":"E. Nart","doi":"10.5565/publmat6412009","DOIUrl":null,"url":null,"abstract":"Let K be a field. For a given valuation on K[x], we determine the structure of its graded algebra and describe its set of key polynomials, in terms of any given key polynomial of minimal degree. We also characterize valuations not admitting key polynomials.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"23","resultStr":"{\"title\":\"Key polynomials over valued fields\",\"authors\":\"E. Nart\",\"doi\":\"10.5565/publmat6412009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let K be a field. For a given valuation on K[x], we determine the structure of its graded algebra and describe its set of key polynomials, in terms of any given key polynomial of minimal degree. We also characterize valuations not admitting key polynomials.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2018-03-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"23\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5565/publmat6412009\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5565/publmat6412009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let K be a field. For a given valuation on K[x], we determine the structure of its graded algebra and describe its set of key polynomials, in terms of any given key polynomial of minimal degree. We also characterize valuations not admitting key polynomials.
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