二次域的显式kummer理论

IF 0.2 Q4 MATHEMATICS

JP Journal of Algebra Number Theory and Applications Pub Date : 2021-04-20 DOI:10.17654/NT050020151

F. Hörmann, Antonella Perucca, Pietro Sgobba, S. Tronto

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引用次数: 1

摘要

设K是一个二次数域，设α∈K，我们给出了一个显式有限过程来一次计算n,m > 1且n | m的所有Kummer度[K(ζm, n√α): K(ζm)]，其中，ζm表示单位的原始m次根。我们也可以用kx的任意有限生成子群来代替α。

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EXPLICIT KUMMER THEORY FOR QUADRATIC FIELDS

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×.

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来源期刊

JP Journal of Algebra Number Theory and Applications MATHEMATICS-

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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.