论文标题
基于纯数字的整体基础
On integral basis of pure number fields
论文作者
论文摘要
Let $K=\mathbb{Q}(\sqrt[n]{a})$ be an extension of degree $n$ of the field $\Q$ of rational numbers, where the integer $a$ is such that for each prime $p$ dividing $n$ either $p\nmid a$ or the highest power of $p$ dividing $a$ is coprime to $p$;当$ a，n $是企业或$ a $无平方的情况下，显然可以满足此条件。本文为$ k $的整体基础提供了明确的构建以及应用程序。 $ k $的整体基础的构造扩展了结果[J.数字理论，{173}（2017），129-146]关于$ \ mathbb {q}的整体基础的周期性，当$ a $ a $是squarefree时。
Let $K=\mathbb{Q}(\sqrt[n]{a})$ be an extension of degree $n$ of the field $\Q$ of rational numbers, where the integer $a$ is such that for each prime $p$ dividing $n$ either $p\nmid a$ or the highest power of $p$ dividing $a$ is coprime to $p$; this condition is clearly satisfied when $a, n$ are coprime or $a$ is squarefree. The present paper gives explicit construction of an integral basis of $K$ along with applications. This construction of an integral basis of $K$ extends a result proved in [J. Number Theory, {173} (2017), 129-146] regarding periodicity of integral bases of $\mathbb{Q}(\sqrt[n]{a})$ when $a$ is squarefree.
