{"title":"有限阿贝尔扩展中的完全正规元","authors":"J. Koo, D. Shin","doi":"10.2478/s11533-013-0280-2","DOIUrl":null,"url":null,"abstract":"We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"13 1","pages":"1725-1731"},"PeriodicalIF":0.0000,"publicationDate":"2013-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Completely normal elements in some finite abelian extensions\",\"authors\":\"J. Koo, D. Shin\",\"doi\":\"10.2478/s11533-013-0280-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.\",\"PeriodicalId\":50988,\"journal\":{\"name\":\"Central European Journal of Mathematics\",\"volume\":\"13 1\",\"pages\":\"1725-1731\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Central European Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/s11533-013-0280-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Central European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/s11533-013-0280-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Completely normal elements in some finite abelian extensions
We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.
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