{"title":"论分离超越基的计算","authors":"R. Steinwandt","doi":"10.1145/377626.377632","DOIUrl":null,"url":null,"abstract":"Let <i>k</i>(<i>x</i><inf>1</inf>,…, <i>x<inf>n</inf></i>)/<i>k</i> be a finitely generated field extension, and <i>g</i><inf>1</inf>,…,<i>g<inf>r</inf></i> ε <i>k</i>(x). For <i>k</i>(<i>x</i><inf>1</inf>,…,<i>x<inf>n</inf></i>)/<i>k</i>(<i>g</i><inf>1</inf>,…,<i>g<inf>r</inf></i>) being separably generated (which in particular includes the case char(<i>k</i>) = 0) we give a method to compute the transcendence degree and a separating transcendence basis of this extension by means of simple linear algebra techniques.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"On computing a separating transcendence basis\",\"authors\":\"R. Steinwandt\",\"doi\":\"10.1145/377626.377632\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <i>k</i>(<i>x</i><inf>1</inf>,…, <i>x<inf>n</inf></i>)/<i>k</i> be a finitely generated field extension, and <i>g</i><inf>1</inf>,…,<i>g<inf>r</inf></i> ε <i>k</i>(x). For <i>k</i>(<i>x</i><inf>1</inf>,…,<i>x<inf>n</inf></i>)/<i>k</i>(<i>g</i><inf>1</inf>,…,<i>g<inf>r</inf></i>) being separably generated (which in particular includes the case char(<i>k</i>) = 0) we give a method to compute the transcendence degree and a separating transcendence basis of this extension by means of simple linear algebra techniques.\",\"PeriodicalId\":314801,\"journal\":{\"name\":\"SIGSAM Bull.\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2000-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIGSAM Bull.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/377626.377632\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIGSAM Bull.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/377626.377632","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let k(x1,…, xn)/k be a finitely generated field extension, and g1,…,gr ε k(x). For k(x1,…,xn)/k(g1,…,gr) being separably generated (which in particular includes the case char(k) = 0) we give a method to compute the transcendence degree and a separating transcendence basis of this extension by means of simple linear algebra techniques.
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