幂积分基循环立方场的表征

IF 0.4 4区数学 Q4 MATHEMATICS

Kodai Mathematical Journal Pub Date : 2019-12-06 DOI:10.2996/kmj44204

Tomokazu Kashio, Ryutaro Sekigawa

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引用次数: 8

摘要

我们为任何循环三次域的整数环的单胚性提供了一个等价条件。我们证明了如果一个循环三次域是单基因的，那么它是最简单的三次域$K_t$，它是Shanks三次多项式$f_t（x）：=x^3-tx^2-（t+3）x-1$与$t\in\mathbb Z$的分裂域。此外，我们给出了$K_t$是单基因的等价条件，它是用$t$显式写成的。

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The characterization of cyclic cubic fields with power integral bases

We provide an equivalent condition for the monogenity of the ring of integers of any cyclic cubic field. We show that if a cyclic cubic field is monogenic then it is a simplest cubic field $K_t$ which is the splitting field of a Shanks cubic polynomial $f_t(x):=x^3-tx^2-(t + 3)x-1$ with $t \in \mathbb Z$. Moreover we give an equivalent condition for when $K_t$ is monogenic, which is explicitly written in terms of $t$.

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来源期刊

Kodai Mathematical Journal 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Kodai Mathematical Journal is edited by the Department of Mathematics, Tokyo Institute of Technology. The journal was issued from 1949 until 1977 as Kodai Mathematical Seminar Reports, and was renewed in 1978 under the present name. The journal is published three times yearly and includes original papers in mathematics.