小度数域的指标及其计算

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI:10.2298/aadm191025032b

A. Bayad, M. Seddik

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引用次数: 0

摘要

设K是一个数字域。研究了Dedekind和Gunji-McQuillan分别引入的K的I(K)和I(K)指标。设n为正整数，我们证明对于任意素数p ?n，存在一个n / Q次的数域使得p除i(K)这个结果类似于Bauer对i(K)的结果。我们计算I(K)和I(K)的三次域和最简单数域的无限族的次数小于7。我们解决了问题并证明了b[1]中提出的猜想。

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On the indices in number fields and their computation for small degrees

Let K be a number field. We investigate the indices I(K) and i(K) of K introduced respectively by Dedekind and Gunji-McQuillan. Let n be a positif integer, we then prove that for any prime p ? n, there exists K a number field of degree n over Q such that p divide i(K). This result is an analogue to Bauer''s one for i(K). We compute I(K) and i(K) for cubic fields and infinite families of simplest number fields of degree less than 7. We solve questions and disprove the conjecture stated in [1].

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).