F. Hörmann, Antonella Perucca, Pietro Sgobba, S. Tronto
{"title":"二次域的显式kummer理论","authors":"F. Hörmann, Antonella Perucca, Pietro Sgobba, S. Tronto","doi":"10.17654/NT050020151","DOIUrl":null,"url":null,"abstract":"LetK be a quadratic number field and let α ∈ K. We present an explicit finite procedure to compute at once all Kummer degrees [K(ζm, n √ α) : K(ζm)] for n,m > 1 with n | m, where ζm denotes a primitive m-th root of unity. We can also replace α by any finitely generated subgroup of K×.","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"1 1","pages":"151-178"},"PeriodicalIF":0.2000,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"EXPLICIT KUMMER THEORY FOR QUADRATIC FIELDS\",\"authors\":\"F. Hörmann, Antonella Perucca, Pietro Sgobba, S. Tronto\",\"doi\":\"10.17654/NT050020151\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"LetK be a quadratic number field and let α ∈ K. We present an explicit finite procedure to compute at once all Kummer degrees [K(ζm, n √ α) : K(ζm)] for n,m > 1 with n | m, where ζm denotes a primitive m-th root of unity. We can also replace α by any finitely generated subgroup of K×.\",\"PeriodicalId\":43248,\"journal\":{\"name\":\"JP Journal of Algebra Number Theory and Applications\",\"volume\":\"1 1\",\"pages\":\"151-178\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2021-04-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"JP Journal of Algebra Number Theory and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17654/NT050020151\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"JP Journal of Algebra Number Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17654/NT050020151","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
LetK be a quadratic number field and let α ∈ K. We present an explicit finite procedure to compute at once all Kummer degrees [K(ζm, n √ α) : K(ζm)] for n,m > 1 with n | m, where ζm denotes a primitive m-th root of unity. We can also replace α by any finitely generated subgroup of K×.
期刊介绍:
The JP Journal of Algebra, Number Theory and Applications is a peer-reviewed international journal. Original research papers theoretical, computational or applied, in nature, in any branch of Algebra and Number Theory are considered by the JPANTA. Together with the core topics in these fields along with their interplay, the journal promotes contributions in Diophantine equations, Representation theory, and Cryptography. Realising the need of wide range of information for any emerging area of potential research, the journal encourages the submission of related survey articles as well.